Abstract group data - 5878656.d

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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': '2.1', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 252, 'aut_gen_orders': [18, 18], 'aut_gens': [[2436660170597917707, 15369454693699625762], [43285313938213756346, 43280067917879648669], [4991228201933320585, 51084895941784892611]], 'aut_group': '5878656.d', 'aut_hash': 9080663322717296588, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5878656, 'aut_permdeg': 567, 'aut_perms': [297585268987954807331095061306229228590564399986559528131118623962270248993705377619266212964630055717366006246092579785900467101393715179133617833034648988428208338395776539344948086306507398212942997863806201675640886919796265491407636240898922180816944879535441705150715371043032210493186388516229968503139454317796107647592607821892632057171678342118207755015192485822092504089434552696917667184674218800514978807465106604690621910357325608664395552999117091129248671700955358806435663875992077116104443495082431761135617313805867312817039653320968420766438590737138423938121543398417040442803371545172036808378330852082081883573422714962485857241157471966031901604088358708935687226162124407203292720540368106653354152344221824952750623214428481266766074714410192048554032186751838997733379564097007732924304725011659625589483784367671301093530500527584112787935913010770992861079122722407665208335272938667474758837496219044779490919673143218832507513668632086975961021930691896013370241520068615600956971197273436316079167203963061566181264328702567806871549928766288660981466926840916435670073761065522885309332938388994010808846675911225276829219095858749995170158929328653030971188118419679200636058042753109650398889243820062372554234853193988913026434494076564254505643212767939468836919335796492581177513, 404229646046272326749593907796506155873711136318548871223350255912705545609943708293774465267152116882905491850778716498130382066512144784335815772079632027770886871778534895523276861341822664746684513221885390607689032827901527678641997580689708720816118048087374632537224334889066400214957589366497986823532849943149531894689171299215930314286775449240176920712177720648230239409541721083676204519136578264238817693174320118418159630785921177831250590723962559860195479674654268315031123252219341685561431965418751253997611998139360961675268288352529319343225624528780156058819006844452810888643289625590359781127272629842891238484870425433554175191387550088337788927270621847503151554347125278175552371340357770339560242662463379155931519030121307505361569451242690864112587847892430855543019846230000112599940720080993178608743603876901375397946916008733482875236600840033249772556882978355043950661517102011054806141339550873150592645093600271838054633012290191705913888724752856088685590258551794680297910227718151605803308795989757817071119476298304083596068366794255882070342537391284195306253208960815855524506699333276514945348640608806056697567066499874820613085094818748567882075025170671627076877200512568699036896694118855244735511788488461667193037177138268017469673295290074262987947419472331359359901], 'aut_phi_ratio': 3.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 189, 1, 1], [2, 378, 1, 1], [2, 567, 1, 1], [2, 1134, 1, 1], [2, 2187, 1, 1], [2, 3402, 1, 1], [2, 10206, 1, 1], [3, 14, 1, 1], [3, 16, 1, 1], [3, 56, 1, 3], [3, 84, 1, 1], [3, 112, 1, 2], [3, 224, 1, 1], [3, 336, 1, 3], [3, 448, 1, 1], [3, 18144, 1, 1], [3, 36288, 1, 1], [4, 13608, 1, 1], [4, 20412, 1, 1], [4, 40824, 1, 2], [4, 61236, 1, 1], [4, 122472, 1, 1], [6, 756, 1, 3], [6, 1512, 1, 8], [6, 3024, 1, 9], [6, 3402, 1, 1], [6, 4536, 1, 6], [6, 6048, 1, 8], [6, 6804, 1, 2], [6, 9072, 1, 2], [6, 12096, 1, 1], [6, 13608, 1, 2], [6, 18144, 1, 3], [6, 27216, 1, 2], [6, 40824, 1, 2], [6, 54432, 1, 1], [6, 108864, 1, 1], [6, 163296, 1, 1], [6, 489888, 1, 1], [7, 139968, 1, 2], [9, 36288, 1, 4], [9, 72576, 1, 4], [12, 27216, 1, 5], [12, 40824, 1, 2], [12, 54432, 1, 4], [12, 81648, 1, 5], [12, 122472, 1, 1], [12, 163296, 1, 2], [12, 244944, 1, 1], [14, 419904, 1, 2], [18, 108864, 1, 3], [18, 326592, 1, 1], [21, 279936, 1, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 252, 'autcentquo_group': '5878656.d', 'autcentquo_hash': 9080663322717296588, 'autcentquo_nilpotent': False, 'autcentquo_order': 5878656, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'cc_stats': [[1, 1, 1], [2, 189, 1], [2, 378, 1], [2, 567, 1], [2, 1134, 1], [2, 2187, 1], [2, 3402, 1], [2, 10206, 1], [3, 14, 1], [3, 16, 1], [3, 56, 3], [3, 84, 1], [3, 112, 2], [3, 224, 1], [3, 336, 3], [3, 448, 1], [3, 18144, 1], [3, 36288, 1], [4, 13608, 1], [4, 20412, 1], [4, 40824, 2], [4, 61236, 1], [4, 122472, 1], [6, 756, 3], [6, 1512, 8], [6, 3024, 9], [6, 3402, 1], [6, 4536, 6], [6, 6048, 8], [6, 6804, 2], [6, 9072, 2], [6, 12096, 1], [6, 13608, 2], [6, 18144, 3], [6, 27216, 2], [6, 40824, 2], [6, 54432, 1], [6, 108864, 1], [6, 163296, 1], [6, 489888, 1], [7, 139968, 2], [9, 36288, 4], [9, 72576, 4], [12, 27216, 5], [12, 40824, 2], [12, 54432, 4], [12, 81648, 5], [12, 122472, 1], [12, 163296, 2], [12, 244944, 1], [14, 419904, 2], [18, 108864, 3], [18, 326592, 1], [21, 279936, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '5878656.d', 'commutator_count': 1, 'commutator_label': '2939328.a', 'complements_known': False, 'complete': True, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '168.42'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 189, 1, 1], [2, 378, 1, 1], [2, 567, 1, 1], [2, 1134, 1, 1], [2, 2187, 1, 1], [2, 3402, 1, 1], [2, 10206, 1, 1], [3, 14, 1, 1], [3, 16, 1, 1], [3, 56, 1, 3], [3, 84, 1, 1], [3, 112, 1, 2], [3, 224, 1, 1], [3, 336, 1, 3], [3, 448, 1, 1], [3, 18144, 1, 1], [3, 36288, 1, 1], [4, 13608, 1, 1], [4, 20412, 1, 1], [4, 40824, 1, 2], [4, 61236, 1, 1], [4, 122472, 1, 1], [6, 756, 1, 3], [6, 1512, 1, 8], [6, 3024, 1, 9], [6, 3402, 1, 1], [6, 4536, 1, 6], [6, 6048, 1, 8], [6, 6804, 1, 2], [6, 9072, 1, 2], [6, 12096, 1, 1], [6, 13608, 1, 2], [6, 18144, 1, 3], [6, 27216, 1, 2], [6, 40824, 1, 2], [6, 54432, 1, 1], [6, 108864, 1, 1], [6, 163296, 1, 1], [6, 489888, 1, 1], [7, 139968, 2, 1], [9, 36288, 1, 4], [9, 72576, 1, 4], [12, 27216, 1, 5], [12, 40824, 1, 2], [12, 54432, 1, 4], [12, 81648, 1, 5], [12, 122472, 1, 1], [12, 163296, 1, 2], [12, 244944, 1, 1], [14, 419904, 2, 1], [18, 108864, 1, 3], [18, 326592, 1, 1], [21, 279936, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 252, 'exponents_of_order': [8, 7, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[14, 1, 4], [16, 1, 1], [28, 1, 2], [42, 1, 4], [48, 0, 2], [56, 1, 12], [84, 1, 12], [96, 1, 1], [112, 1, 11], [128, 1, 1], [168, 1, 18], [224, 1, 6], [336, 1, 16], [448, 1, 4], [672, 1, 3], [896, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '5878656.d', 'hash': 9080663322717296588, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 252, 'inner_gen_orders': [18, 18], 'inner_gens': [[2436660170597917707, 46097091137594724955], [30734816622106947596, 15369454693699625762]], 'inner_hash': 9080663322717296588, 'inner_nilpotent': False, 'inner_order': 5878656, 'inner_split': True, 'inner_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'inner_used': [1, 2], 'irrC_degree': 14, 'irrQ_degree': 14, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 2], [3, 4], [6, 2], [7, 6], [8, 2], [14, 6], [16, 1], [21, 4], [28, 2], [42, 4], [48, 2], [56, 12], [84, 12], [96, 1], [112, 11], [128, 1], [168, 18], [224, 6], [336, 16], [448, 4], [672, 3], [896, 1]], 'label': '5878656.d', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C3^7.C2^4:GL(3,2)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 120, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 120, 'number_divisions': 117, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 5878656, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 18063], [3, 56618], [4, 299376], [6, 1198638], [7, 279936], [9, 435456], [12, 1537704], [14, 839808], [18, 653184], [21, 559872]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': None, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [6, 4], [7, 6], [8, 2], [14, 6], [16, 1], [21, 4], [28, 2], [42, 4], [56, 12], [84, 12], [96, 2], [112, 11], [128, 1], [168, 18], [224, 6], [336, 16], [448, 4], [672, 3], [896, 1]], 'representations': {'Perm': {'d': 21, 'gens': [15369454693699625762, 2436660170597917707]}}, 'schur_multiplier': [2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 128, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^7.C_2^4:\\GL(3,2)', 'transitive_degree': 21, '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: 38737678
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 4, 'group_order': 5878656, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 38737710
    {'aut_label': '2A', 'centralizer': None, 'counter': 2, 'group_counter': 4, 'group_order': 5878656, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 5065, 'size': 189}
  • id: 38737721
    {'aut_label': '2B', 'centralizer': None, 'counter': 3, 'group_counter': 4, 'group_order': 5878656, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 281653164984, 'size': 378}
  • id: 38737732
    {'aut_label': '2C', 'centralizer': None, 'counter': 4, 'group_counter': 4, 'group_order': 5878656, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 121645100492294426, 'size': 567}
  • id: 38737743
    {'aut_label': '2D', 'centralizer': None, 'counter': 5, 'group_counter': 4, 'group_order': 5878656, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 33287075950992434373, 'size': 1134}
  • id: 38737754
    {'aut_label': '2E', 'centralizer': '2187.A', 'counter': 6, 'group_counter': 4, 'group_order': 5878656, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 4988181594995429309, 'size': 2187}
  • id: 38737765
    {'aut_label': '2F', 'centralizer': None, 'counter': 7, 'group_counter': 4, 'group_order': 5878656, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 6045666750449134, 'size': 3402}
  • id: 38737776
    {'aut_label': '2G', 'centralizer': None, 'counter': 8, 'group_counter': 4, 'group_order': 5878656, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 17801577871356021149, 'size': 10206}
  • id: 38737787
    {'aut_label': '3A', 'centralizer': '14.D', 'counter': 9, 'group_counter': 4, 'group_order': 5878656, 'label': '3A', 'order': 3, 'powers': [9, 1, 9], 'representative': 79833600, 'size': 14}
  • id: 38737679
    {'aut_label': '3B', 'centralizer': '16.A', 'counter': 10, 'group_counter': 4, 'group_order': 5878656, 'label': '3B', 'order': 3, 'powers': [10, 1, 10], 'representative': 2555258657878125603, 'size': 16}
  • id: 38737690
    {'aut_label': '3C', 'centralizer': '56.C', 'counter': 11, 'group_counter': 4, 'group_order': 5878656, 'label': '3C', 'order': 3, 'powers': [11, 1, 11], 'representative': 174436496880, 'size': 56}
  • id: 38737701
    {'aut_label': '3D', 'centralizer': '56.D', 'counter': 12, 'group_counter': 4, 'group_order': 5878656, 'label': '3D', 'order': 3, 'powers': [12, 1, 12], 'representative': 174436496784, 'size': 56}
  • id: 38737703
    {'aut_label': '3E', 'centralizer': '56.U', 'counter': 13, 'group_counter': 4, 'group_order': 5878656, 'label': '3E', 'order': 3, 'powers': [13, 1, 13], 'representative': 4866515391209472004, 'size': 56}
  • id: 38737704
    {'aut_label': '3F', 'centralizer': '84.L', 'counter': 14, 'group_counter': 4, 'group_order': 5878656, 'label': '3F', 'order': 3, 'powers': [14, 1, 14], 'representative': 45600, 'size': 84}
  • id: 38737705
    {'aut_label': '3G', 'centralizer': '112.P', 'counter': 15, 'group_counter': 4, 'group_order': 5878656, 'label': '3G', 'order': 3, 'powers': [15, 1, 15], 'representative': 4866180720020121843, 'size': 112}
  • id: 38737706
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  • id: 38737707
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  • id: 38737708
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  • id: 38737709
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  • id: 38737711
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  • id: 38737712
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  • id: 38737713
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  • id: 38737714
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  • id: 38737715
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  • id: 38737716
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  • id: 38737717
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  • id: 38737718
    {'aut_label': '4D', 'centralizer': None, 'counter': 27, 'group_counter': 4, 'group_order': 5878656, 'label': '4D', 'order': 4, 'powers': [7, 27, 27], 'representative': 7804494291439220424, 'size': 40824}
  • id: 38737719
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  • id: 38737720
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  • id: 38737722
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  • id: 38737723
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  • id: 38737724
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  • id: 38737725
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  • id: 38737726
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  • id: 38737727
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  • id: 38737728
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  • id: 38737729
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  • id: 38737730
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  • id: 38737731
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  • id: 38737733
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  • id: 38737734
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  • id: 38737735
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  • id: 38737736
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  • id: 38737737
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  • id: 38737738
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  • id: 38737739
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  • id: 38737740
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  • id: 38737741
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  • id: 38737742
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  • id: 38737744
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  • id: 38737745
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  • id: 38737746
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  • id: 38737747
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  • id: 38737748
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  • id: 38737749
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  • id: 38737750
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  • id: 38737751
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  • id: 38737752
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  • id: 38737753
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  • id: 38737755
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  • id: 38737756
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  • id: 38737757
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  • id: 38737758
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  • id: 38737759
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  • id: 38737760
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  • id: 38737761
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  • id: 38737762
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  • id: 38737763
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  • id: 38737764
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  • id: 38737766
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  • id: 38737767
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  • id: 38737768
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  • id: 38737769
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  • id: 38737770
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  • id: 38737771
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  • id: 38737772
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  • id: 38737773
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  • id: 38737774
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  • id: 38737775
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  • id: 38737777
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  • id: 38737778
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  • id: 38737779
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  • id: 38737780
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  • id: 38737781
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  • id: 38737782
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  • id: 38737783
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  • id: 38737784
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  • id: 38737785
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  • id: 38737786
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  • id: 38737788
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  • id: 38737789
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  • id: 38737790
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  • id: 38737791
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  • id: 38737792
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  • id: 38737793
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  • id: 38737794
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  • id: 38737795
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  • id: 38737796
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  • id: 38737797
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  • id: 38737680
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  • id: 38737681
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  • id: 38737682
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  • id: 38737683
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  • id: 38737684
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  • id: 38737685
    {'aut_label': '12M', 'centralizer': None, 'counter': 105, 'group_counter': 4, 'group_order': 5878656, 'label': '12M', 'order': 12, 'powers': [40, 26, 105], 'representative': 38538531908793907055, 'size': 81648}
  • id: 38737686
    {'aut_label': '12N', 'centralizer': None, 'counter': 106, 'group_counter': 4, 'group_order': 5878656, 'label': '12N', 'order': 12, 'powers': [70, 27, 106], 'representative': 12552787148779658885, 'size': 81648}
  • id: 38737687
    {'aut_label': '12O', 'centralizer': None, 'counter': 107, 'group_counter': 4, 'group_order': 5878656, 'label': '12O', 'order': 12, 'powers': [65, 25, 107], 'representative': 46220247078029718358, 'size': 81648}
  • id: 38737688
    {'aut_label': '12P', 'centralizer': None, 'counter': 108, 'group_counter': 4, 'group_order': 5878656, 'label': '12P', 'order': 12, 'powers': [66, 27, 108], 'representative': 4870339118583304077, 'size': 81648}
  • id: 38737689
    {'aut_label': '12Q', 'centralizer': None, 'counter': 109, 'group_counter': 4, 'group_order': 5878656, 'label': '12Q', 'order': 12, 'powers': [50, 28, 109], 'representative': 51086030171589446398, 'size': 122472}
  • id: 38737691
    {'aut_label': '12R', 'centralizer': None, 'counter': 110, 'group_counter': 4, 'group_order': 5878656, 'label': '12R', 'order': 12, 'powers': [75, 27, 110], 'representative': 7682870395509286443, 'size': 163296}
  • id: 38737692
    {'aut_label': '12S', 'centralizer': None, 'counter': 111, 'group_counter': 4, 'group_order': 5878656, 'label': '12S', 'order': 12, 'powers': [41, 26, 111], 'representative': 46220602490031992375, 'size': 163296}
  • id: 38737693
    {'aut_label': '12T', 'centralizer': None, 'counter': 112, 'group_counter': 4, 'group_order': 5878656, 'label': '12T', 'order': 12, 'powers': [70, 29, 112], 'representative': 4991207090764118547, 'size': 244944}
  • id: 38737694
    {'aut_label': '14A1', 'centralizer': None, 'counter': 113, 'group_counter': 4, 'group_order': 5878656, 'label': '14A1', 'order': 14, 'powers': [83, 114, 6], 'representative': 33170697042457691045, 'size': 419904}
  • id: 38737695
    {'aut_label': '14A-1', 'centralizer': None, 'counter': 114, 'group_counter': 4, 'group_order': 5878656, 'label': '14A-1', 'order': 14, 'powers': [84, 113, 6], 'representative': 20357259297187882319, 'size': 419904}
  • id: 38737696
    {'aut_label': '18A', 'centralizer': None, 'counter': 115, 'group_counter': 4, 'group_order': 5878656, 'label': '18A', 'order': 18, 'powers': [85, 57, 115], 'representative': 38540799241435900107, 'size': 108864}
  • id: 38737697
    {'aut_label': '18B', 'centralizer': None, 'counter': 116, 'group_counter': 4, 'group_order': 5878656, 'label': '18B', 'order': 18, 'powers': [86, 57, 116], 'representative': 15489187404425821895, 'size': 108864}
  • id: 38737698
    {'aut_label': '18C', 'centralizer': None, 'counter': 117, 'group_counter': 4, 'group_order': 5878656, 'label': '18C', 'order': 18, 'powers': [88, 57, 117], 'representative': 27919617232937714637, 'size': 108864}
  • id: 38737699
    {'aut_label': '18D', 'centralizer': None, 'counter': 118, 'group_counter': 4, 'group_order': 5878656, 'label': '18D', 'order': 18, 'powers': [87, 51, 118], 'representative': 2434392187419351842, 'size': 326592}
  • id: 38737700
    {'aut_label': '21A1', 'centralizer': None, 'counter': 119, 'group_counter': 4, 'group_order': 5878656, 'label': '21A1', 'order': 21, 'powers': [119, 83, 10], 'representative': 50969275860191678784, 'size': 279936}
  • id: 38737702
    {'aut_label': '21A-1', 'centralizer': None, 'counter': 120, 'group_counter': 4, 'group_order': 5878656, 'label': '21A-1', 'order': 21, 'powers': [120, 84, 10], 'representative': 25484870552241174357, 'size': 279936}
• group 5878656.d does not appear in gps_qchar
• group 5878656.d does not appear in gps_char
• 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: 6278199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 5878656, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 42, 'label': '5878656.d.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5878656.d', 'subgroup_hash': 9080663322717296588, 'subgroup_order': 5878656, 'subgroup_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 6278310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 2939328, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': True, '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': False, 'special_labels': ['D', 'PC', 'L1', 'D1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2939328.a', 'subgroup_hash': 8772485648577800496, 'subgroup_order': 2939328, 'subgroup_tex': 'C_3^7.C_2^3:\\GL(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 6278323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '5878656.d.7.A', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.aB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '839808.hh', 'subgroup_hash': 7906437786084384351, 'subgroup_order': 839808, 'subgroup_tex': 'C_3^7.C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '5878656.d.7.B', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.aC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '839808.hf', 'subgroup_hash': 6234311676403603730, 'subgroup_order': 839808, 'subgroup_tex': 'C_3^7.C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.8.A', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '734832.a', 'subgroup_hash': 6385344614509044200, 'subgroup_order': 734832, 'subgroup_tex': 'C_3^7.F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.8.B', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '734832.b', 'subgroup_hash': 7351513752362711127, 'subgroup_order': 734832, 'subgroup_tex': 'C_3^6.(S_3\\times \\GL(3,2))', 'supersolvable': False, 'sylow': 0}
  • id: 6278367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.8.C', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '734832.c', 'subgroup_hash': 1907405768926397352, 'subgroup_order': 734832, 'subgroup_tex': 'C_3^7.(C_2\\times \\GL(3,2))', 'supersolvable': False, 'sylow': 0}
  • id: 6278378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.fv', 'subgroup_hash': 8899482030819059829, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^7.C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.hk', 'subgroup_hash': 4672052325425288161, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^4.S_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.bl', 'subgroup_hash': 7327310878096809880, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^7.C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.bj', 'subgroup_hash': 4782122066513349204, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^7.C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.eB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.fu', 'subgroup_hash': 1153129233125313688, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^7.C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.eC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.ft', 'subgroup_hash': 8241887531883778153, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^7.C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.fB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.bm', 'subgroup_hash': 3633228560188170168, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^7.C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.fC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.bg', 'subgroup_hash': 6166490738288754801, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^7.C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.gB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.bf', 'subgroup_hash': 1788049712601208105, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^4.C_6^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.14.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.gC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '419904.bk', 'subgroup_hash': 8630631229725329553, 'subgroup_order': 419904, 'subgroup_tex': 'C_3^7.C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.16.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '367416.c', 'subgroup_hash': 3781095278222425392, 'subgroup_order': 367416, 'subgroup_tex': 'C_3^7.\\PSL(2,7)', 'supersolvable': False, 'sylow': 0}
  • id: 6278299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.16.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '367416.b', 'subgroup_hash': 8954445750122135999, 'subgroup_order': 367416, 'subgroup_tex': 'C_3^7.F_8:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 6278311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.16.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': True, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '367416.a', 'subgroup_hash': 4140644034209362342, 'subgroup_order': 367416, 'subgroup_tex': 'C_3^7.\\GL(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 6278314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.21.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '21.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '279936.f', 'subgroup_hash': 5103271749500440600, 'subgroup_order': 279936, 'subgroup_tex': 'C_3^6.C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.21.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '21.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '279936.z', 'subgroup_hash': 2549359548974983920, 'subgroup_order': 279936, 'subgroup_tex': 'C_3^2.S_3^5:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '244944.b', 'subgroup_hash': 3251838267212006343, 'subgroup_order': 244944, 'subgroup_tex': 'C_3^7:(C_2\\times F_8)', 'supersolvable': False, 'sylow': 0}
  • id: 6278317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '244944.a', 'subgroup_hash': 390404346474216465, 'subgroup_order': 244944, 'subgroup_tex': 'C_3^6:(C_2\\times \\GL(3,2))', 'supersolvable': False, 'sylow': 0}
  • id: 6278318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.df', 'subgroup_hash': 3385776665686710738, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^6.(D_6\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.el', 'subgroup_hash': 4905905475156125026, 'subgroup_order': 209952, 'subgroup_tex': 'C_3\\wr S_4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.fd', 'subgroup_hash': 2420212589261764445, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^4.S_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.x', 'subgroup_hash': 2654541563172986090, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^7.C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.df', 'subgroup_hash': 3385776665686710738, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^6.(D_6\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.ba', 'subgroup_hash': 8825028515236026616, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^7.C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.iv', 'subgroup_hash': 525607828590270037, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^7.C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.z', 'subgroup_hash': 5280994060765535647, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^7.C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.iB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.w', 'subgroup_hash': 7840450613195688085, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^4.C_6^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.iC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.y', 'subgroup_hash': 8313924744156575404, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^7.C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.28.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '209952.ix', 'subgroup_hash': 1515333359091919929, 'subgroup_order': 209952, 'subgroup_tex': 'C_3^7.C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.r', 'subgroup_hash': 4553001237534440894, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6.C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.t', 'subgroup_hash': 4326369945856367978, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6.C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.cb', 'subgroup_hash': 2878836095061012226, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^5.D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.cc', 'subgroup_hash': 753575748815784367, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7:(C_2^4:C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.ca', 'subgroup_hash': 2856064819092500444, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^2.S_3^5:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2687799775436044624, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.bn', 'subgroup_hash': 3042338896259778021, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.bl', 'subgroup_hash': 5519377952685847148, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.j', 'subgroup_hash': 8118045935722796121, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6:C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.j', 'subgroup_hash': 8118045935722796121, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6:C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.bo', 'subgroup_hash': 7029391503515532127, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.bj', 'subgroup_hash': 4454696063351447374, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.o', 'subgroup_hash': 4519463644768039457, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6:C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.c', 'subgroup_hash': 3246291642654537061, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6.C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.cb', 'subgroup_hash': 2878836095061012226, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^5.D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.pB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.ce', 'subgroup_hash': 1417604981334546756, 'subgroup_order': 139968, 'subgroup_tex': 'C_3:S_3^3.S_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 6278348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.pC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.ca', 'subgroup_hash': 2856064819092500444, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^2.S_3^5:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.bn', 'subgroup_hash': 3042338896259778021, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.j', 'subgroup_hash': 8118045935722796121, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6:C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.sB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.bo', 'subgroup_hash': 7029391503515532127, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.sC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.bm', 'subgroup_hash': 5907011102252276827, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.bk', 'subgroup_hash': 3959274225669495494, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^7:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.42.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.o', 'subgroup_hash': 4519463644768039457, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6:C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.48.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': True, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '122472.a', 'subgroup_hash': 5655893543397326836, 'subgroup_order': 122472, 'subgroup_tex': 'C_3^6:\\GL(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 6278357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.48.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '122472.b', 'subgroup_hash': 862536160825238025, 'subgroup_order': 122472, 'subgroup_tex': 'C_3^7:F_8', 'supersolvable': False, 'sylow': 0}
  • id: 6278358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.fz', 'subgroup_hash': 5268408500430882560, 'subgroup_order': 104976, 'subgroup_tex': 'C_3\\wr A_4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.ed', 'subgroup_hash': 6159123886857924079, 'subgroup_order': 104976, 'subgroup_tex': 'C_3\\wr A_4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.bc', 'subgroup_hash': 4249072608285335807, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(C_6\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.gc', 'subgroup_hash': 2094843784941561178, 'subgroup_order': 104976, 'subgroup_tex': 'C_3\\wr S_4.C_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.cc', 'subgroup_hash': 6724099318369674634, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(A_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 6278363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.cb', 'subgroup_hash': 5026771824623500724, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^7.(C_2\\times \\SL(2,3))', 'supersolvable': False, 'sylow': 0}
  • id: 6278364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.be', 'subgroup_hash': 63881089879201090, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^7.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.ef', 'subgroup_hash': 8275005433932975525, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.cd', 'subgroup_hash': 404298558486778831, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.bc', 'subgroup_hash': 4249072608285335807, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(C_6\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.be', 'subgroup_hash': 63881089879201090, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^7.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.cc', 'subgroup_hash': 6724099318369674634, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(A_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 6278371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.eh', 'subgroup_hash': 778749322720519886, 'subgroup_order': 104976, 'subgroup_tex': 'C_3\\wr A_4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.gb', 'subgroup_hash': 7069113189222303811, 'subgroup_order': 104976, 'subgroup_tex': 'C_3\\wr A_4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.bd', 'subgroup_hash': 5491591524198552544, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.jp', 'subgroup_hash': 6275167317065982094, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^7.C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.bd', 'subgroup_hash': 5491591524198552544, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.ef', 'subgroup_hash': 8275005433932975525, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.sB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9037416581089594845, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^4.C_6^2.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.sC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9037416581089594845, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^5.A_4.C_3.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.gd', 'subgroup_hash': 3712651426118948050, 'subgroup_order': 104976, 'subgroup_tex': 'C_3\\wr S_4.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 6278381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.bf', 'subgroup_hash': 465583718472659320, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.bf', 'subgroup_hash': 465583718472659320, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.wB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.cd', 'subgroup_hash': 404298558486778831, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.56.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.wC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.cd', 'subgroup_hash': 404298558486778831, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.63.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '63.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 63, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '93312.bs', 'subgroup_hash': 4704729606666360257, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^4.D_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '91854.c', 'subgroup_hash': 5517587515177415154, 'subgroup_order': 91854, 'subgroup_tex': 'C_3^6.C_{21}:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.hh', 'subgroup_hash': 387072276691456286, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:(D_6\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.cc', 'subgroup_hash': 8681013747633533623, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^4.S_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.cb', 'subgroup_hash': 4400248036626116547, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:(C_2^2\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 553795484890546160, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.b', 'subgroup_hash': 1122828127171948359, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.(C_2^2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.f', 'subgroup_hash': 1421550655586056904, 'subgroup_order': 69984, 'subgroup_tex': '(C_3:S_3)^3.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3827208472977228976, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.c', 'subgroup_hash': 2678508519303637742, 'subgroup_order': 69984, 'subgroup_tex': 'C_3\\wr A_4:C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 6278396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bj', 'subgroup_hash': 5459180036442879570, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bi', 'subgroup_hash': 239091071939790942, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6866045791174802419, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 6278399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8583434785596436590, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 6278201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1581672046515052025, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.nB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.cd', 'subgroup_hash': 7750697101158334252, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^2:S_3^2.S_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 6278203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.nC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.cc', 'subgroup_hash': 8681013747633533623, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^4.S_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.cc', 'subgroup_hash': 8681013747633533623, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^4.S_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.cb', 'subgroup_hash': 4400248036626116547, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:(C_2^2\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 610101116806135082, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278207
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4575913163941816758, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 6278208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.sB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bi', 'subgroup_hash': 239091071939790942, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.sC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bx', 'subgroup_hash': 803415223238403746, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^2:S_3^2.S_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 6278210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bk', 'subgroup_hash': 6433841821967542677, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 6278212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bm', 'subgroup_hash': 2691910879112399039, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bw', 'subgroup_hash': 9073574163382271981, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^2:S_3^2.S_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 6278214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bu', 'subgroup_hash': 632643044954127995, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^4:C_6.D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.h', 'subgroup_hash': 4814747757799365679, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6:C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.h', 'subgroup_hash': 4814747757799365679, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6:C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bg', 'subgroup_hash': 4281342478213573610, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.b', 'subgroup_hash': 1122828127171948359, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.(C_2^2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 34992, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.cb', 'subgroup_hash': 4400248036626116547, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:(C_2^2\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7709344898670018638, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bk', 'subgroup_hash': 6433841821967542677, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 6278223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bm', 'subgroup_hash': 2691910879112399039, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bj', 'subgroup_hash': 5459180036442879570, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bi', 'subgroup_hash': 239091071939790942, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bp', 'subgroup_hash': 2823004357242353880, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 6278227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bp', 'subgroup_hash': 2823004357242353880, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 6278228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bl', 'subgroup_hash': 9014406854253293391, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 6278229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bn', 'subgroup_hash': 9033578157714315977, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^4:C_6^2.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 6278230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.blB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bj', 'subgroup_hash': 5459180036442879570, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.blC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bw', 'subgroup_hash': 9073574163382271981, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^2:S_3^2.S_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 6278232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bl', 'subgroup_hash': 9014406854253293391, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 6278234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bn', 'subgroup_hash': 9033578157714315977, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^4:C_6^2.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 6278235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3011813159208600103, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bg', 'subgroup_hash': 4281342478213573610, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.p', 'subgroup_hash': 6223392654250980061, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bq', 'subgroup_hash': 451931391387674455, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^4.C_6^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bo', 'subgroup_hash': 4951314155353507066, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^4.C_6^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.m', 'subgroup_hash': 1356545172062492268, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^4.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 6278241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.m', 'subgroup_hash': 1356545172062492268, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^4.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 6278242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8539133172911397809, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.p', 'subgroup_hash': 6223392654250980061, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.p', 'subgroup_hash': 6223392654250980061, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bh', 'subgroup_hash': 5502654455259084544, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.h', 'subgroup_hash': 4814747757799365679, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6:C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.caB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bv', 'subgroup_hash': 7772351334121914974, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^4:C_6.D_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.caC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.bh', 'subgroup_hash': 5502654455259084544, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^7:C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3459225808763334297, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 6278251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.84.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '69984.n', 'subgroup_hash': 3043011397886974253, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3676449550061675661, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 6278253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.ex', 'subgroup_hash': 2100008257463756398, 'subgroup_order': 52488, 'subgroup_tex': 'C_3\\wr A_4.C_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.bx', 'subgroup_hash': 2531877316727552763, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.(C_6\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.eh', 'subgroup_hash': 3605677154637666272, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.bx', 'subgroup_hash': 2531877316727552763, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.(C_6\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.fe', 'subgroup_hash': 6233682747017440308, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.gB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8552820122335554285, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.A_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.gC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8552820122335554285, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.A_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.ff', 'subgroup_hash': 5420192225667659674, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.iB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4175660285741812225, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.C_6^2.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 6278263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.iC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4175660285741812225, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.C_6^2.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 6278264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.ez', 'subgroup_hash': 2821033090217949726, 'subgroup_order': 52488, 'subgroup_tex': 'C_3\\wr A_4.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 6278265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.fc', 'subgroup_hash': 7161753922226767577, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.fc', 'subgroup_hash': 7161753922226767577, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.mB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8191588946374615359, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_6^2:C_3.C_6', 'supersolvable': False, 'sylow': 0}
  • id: 6278269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.mC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8191588946374615359, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^3.C_6^2.C_3^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 6278270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.by', 'subgroup_hash': 4894500697377149961, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.bw', 'subgroup_hash': 1799004152239064594, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 6278272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.bz', 'subgroup_hash': 1677183523945680450, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.ca', 'subgroup_hash': 8500811763530502757, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.fa', 'subgroup_hash': 8297522179336697251, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.by', 'subgroup_hash': 4894500697377149961, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.tB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.eh', 'subgroup_hash': 3605677154637666272, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.tC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.eh', 'subgroup_hash': 3605677154637666272, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 6278279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.uB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.bz', 'subgroup_hash': 1677183523945680450, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.uC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.bz', 'subgroup_hash': 1677183523945680450, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.fa', 'subgroup_hash': 8297522179336697251, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.wB', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.ca', 'subgroup_hash': 8500811763530502757, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.112.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.wC', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.ca', 'subgroup_hash': 8500811763530502757, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.cu', 'subgroup_hash': 4060382036469568711, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^4.D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.cy', 'subgroup_hash': 2092486441644422636, 'subgroup_order': 46656, 'subgroup_tex': '(C_3:S_3)^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.cq', 'subgroup_hash': 4838733552333219572, 'subgroup_order': 46656, 'subgroup_tex': '(C_3:S_3)^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3112259838574701866, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2108294886796444813, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.y', 'subgroup_hash': 3987093188507500600, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.v', 'subgroup_hash': 6399936725036530197, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.y', 'subgroup_hash': 3987093188507500600, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.v', 'subgroup_hash': 6399936725036530197, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.cu', 'subgroup_hash': 4060382036469568711, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^4.D_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.cq', 'subgroup_hash': 4838733552333219572, 'subgroup_order': 46656, 'subgroup_tex': '(C_3:S_3)^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 6278296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 748096519237621753, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2.C_2^5', 'supersolvable': False, 'sylow': 0}
  • id: 6278297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.y', 'subgroup_hash': 3987093188507500600, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.v', 'subgroup_hash': 6399936725036530197, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.y', 'subgroup_hash': 3987093188507500600, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.126.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '46656.v', 'subgroup_hash': 6399936725036530197, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 6278302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 21, 'label': '5878656.d.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45927.a', 'subgroup_hash': 6192111462583310575, 'subgroup_order': 45927, 'subgroup_tex': 'C_3^6.C_{21}:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 6278303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 34992, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.168.A', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '168.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '168.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,7)', 'simple': False, 'solvable': True, 'special_labels': ['R', 'C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.cf', 'subgroup_hash': 7311488304926548897, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^7:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 6278304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 17496, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.336.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '336.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '336.209', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 209, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\GL(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.ct', 'subgroup_hash': 4607266734920753059, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^7:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 6278305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '5878656.d.896.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '896.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 896, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6561.396911', 'subgroup_hash': 3767471182206527911, 'subgroup_order': 6561, 'subgroup_tex': 'C_3\\times C_3^6.C_3', 'supersolvable': True, 'sylow': 3}
  • id: 6278306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 4374, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.1344.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1344.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1344.11686', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11686, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:\\GL(3,2)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 499107902890008247, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^7.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 6278307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.2187.A', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2187.a1.M', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2187, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2688.cd', 'subgroup_hash': 8270626938983654557, 'subgroup_order': 2688, 'subgroup_tex': 'C_2^4:\\GL(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 6278308
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2187, 'characteristic': True, 'core_order': 2187, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5878656.d.2688.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '2688.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2688.cd', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8270626938983654557, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 2688, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:\\GL(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9310', 'subgroup_hash': 812665320891796152, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^7', 'supersolvable': True, 'sylow': 0}
  • id: 6278309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '5878656.d.45927.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '45927.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45927, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 6278312
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '5878656.d.839808.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '839808.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 839808, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 6278313
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5878656.d', 'ambient_counter': 4, 'ambient_order': 5878656, 'ambient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'central': True, 'central_factor': False, 'centralizer_order': 5878656, 'characteristic': True, 'core_order': 1, 'counter': 201, 'cyclic': True, 'direct': None, 'hall': 1, 'label': '5878656.d.5878656.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '5878656.a1.N', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '5878656.d', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9080663322717296588, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 5878656, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^7.C_2^4:\\GL(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', 'C4'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 6278209
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 127335166985681277, 711374856192144, 6230654664, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.P', 'old_label': '84.sC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.U', 'subgroup_fusion': None, 'weyl_group': '139968.ce'}
  • id: 6278210
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [7887, -1, 7166, -1], 'generators': [2554923893160038643, 80784, 2432902014403666081, 43545603, 711374856192144, 376784618192784, 17804267676843183237, 124268757511323333, 20922793521841, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.84.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.t1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.V', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278233
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 35602465491260460988, 711374856192144, 4867293550903742131, 6230654664, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840, 4993474705757833439], 'label': '5878656.d.14.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.B', 'old_label': '14.eC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.F', 'subgroup_fusion': None, 'weyl_group': '839808.hf'}
  • id: 6278234
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 21, 'diagramx': [503, -1, 4812, -1], 'generators': [2554923893160038643, 80784, 17804288599672988157, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bn1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BQ', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278235
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [4731, -1, 6160, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 2560216252372427973, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840, 20354279944770333836], 'label': '5878656.d.84.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bo1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BR', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278208
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902014403666081, 711374856192144, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.84.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.sB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.T', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278199
    {'ambient': '5878656.d', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [163, 6747, 40, 1131], 'generators': [2554923893160038643, 80784, 43283824691770695628, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 2554903171111956601, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '5878656.d'}
  • id: 6278200
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 7, 'diagramx': [609, -1, 571, -1], 'generators': [2554923893160038643, 38540443835888000668, 80784, 43545603, 2432902008180269065, 2288892424371718, 711374856192144, 46097091137594724955, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840, 125423428146146639], 'label': '5878656.d.14.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '14.c1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.C', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278201
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 21, 'diagramx': [4914, -1, 6218, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 376784618192784, 17804267676843183237, 20922793521841, 124268757511328399, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.m1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.M', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278202
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 2560237175122399197, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.84.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.P', 'old_label': '84.nB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.N', 'subgroup_fusion': None, 'weyl_group': '139968.ce'}
  • id: 6278203
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2554923893160038643, 80784, 20354279938546942078, 43545603, 2432902014403666081, 711374856192144, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.nC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.O', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278204
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 21, 'diagramx': [5277, -1, 6334, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 5065, 79833840, 17804288686811362415], 'label': '5878656.d.84.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.o1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.P', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278205
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 21, 'diagramx': [697, -1, 4874, -1], 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 2560216252372427973, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.84.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.p1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.Q', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278206
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 21, 'diagramx': [8827, -1, 7466, -1], 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 2560216252372427973, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.84.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.q1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.R', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278207
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 7, 'diagramx': [8456, -1, 7347, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902014403666081, 711374856192144, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '84.r1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.S', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278211
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 7, 'diagramx': [363, -1, 492, -1], 'generators': [2554923893160038643, 38540443835888000668, 80784, 43545603, 2432902008180269065, 2267882456192636, 711374856192144, 46097091137594724955, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840, 125423428146146639], 'label': '5878656.d.14.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '14.d1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.D', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278212
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [2054, -1, 5306, -1], 'generators': [2554923893160038643, 80784, 17804288599672988157, 43545603, 2432902014403666081, 711374856192144, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.84.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.u1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.W', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278213
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [8290, -1, 7294, -1], 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 2560216252372427973, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.v1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.X', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278214
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [5095, -1, 6276, -1], 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 2560216252372427973, 376784618192784, 20922793521841, 2557526453116059575, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.w1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.Y', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278215
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9555, -1, 7698, -1], 'generators': [2554923893160038643, 43545603, 25483313688004167094, 2432902008180269065, 20929016908825, 711374856192144, 6230649601, 376610217984000, 48530349034036445518, 25483736060594380827, 79833840, 376784618112000], 'label': '5878656.d.84.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '84.x1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.Z', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278216
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [9737, -1, 7756, -1], 'generators': [2554923893160038643, 43545603, 25483313688004167094, 2432902008180269065, 20929016908825, 711374856192144, 6230649601, 48530349033956692558, 376610217984000, 25483736060594380827, 79833840, 376784618112000], 'label': '5878656.d.84.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.C', 'old_label': '84.y1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BA', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 6278217
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 7, 'diagramx': [5677, -1, 6462, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902014403666081, 711374856192144, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.84.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '84.z1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BB', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278218
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [9373, -1, 7640, -1], 'generators': [2432902008180269065, 174400208784, 144, 43545603, 17921734469375609761, 6230654664, 79833840, 80784, 20354279944770293494, 5065, 2554547282942054643, 2554902970373784482], 'label': '5878656.d.84.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.BC', 'old_label': '84.ba1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BC', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278219
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 21, 'diagramx': [880, -1, 4932, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bb1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BD', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278220
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [4549, -1, 6102, -1], 'generators': [2554923893160038643, 80784, 2432902014403666081, 43545603, 711374856192144, 2560237175122399197, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840, 20354279944770333836], 'label': '5878656.d.84.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bc1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BE', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278221
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [7647, -1, 7090, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 127314244155876453, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 20354279938546901732, 79833840], 'label': '5878656.d.84.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bd1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BF', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278222
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 38540443835888000668, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 46097091137594724955, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840, 125423428146146639], 'label': '5878656.d.14.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '14.eB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.E', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278223
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [1848, -1, 5241, -1], 'generators': [2554923893160038643, 80784, 20354279938546942078, 43545603, 2432902014403666081, 711374856192144, 127314244155876453, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.be1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BG', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278224
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [3433, -1, 5746, -1], 'generators': [2554923893160038643, 80784, 2432902014403666081, 43545603, 127335166985681277, 711374856192144, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840, 20354279944770333836], 'label': '5878656.d.84.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bf1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BH', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278225
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [3979, -1, 5920, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 127314244155876453, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840, 20354279944770333836], 'label': '5878656.d.84.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bg1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BI', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278226
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [3034, -1, 5619, -1], 'generators': [2554923893160038643, 80784, 20354279938546942078, 43545603, 2432902014403666081, 711374856192144, 2560237175122399197, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bh1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BJ', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278227
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [3239, -1, 5684, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 2560237175122399197, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 20354279938546901732, 79833840], 'label': '5878656.d.84.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bi1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BK', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278228
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [1255, -1, 5052, -1], 'generators': [2554923893160038643, 80784, 20354279938546942078, 43545603, 2432902014403666081, 127335166985681277, 711374856192144, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bj1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BL', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278229
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [298, -1, 4747, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902014403666081, 127335166985681277, 711374856192144, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 20354279938546901732, 79833840], 'label': '5878656.d.84.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bk1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BM', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278230
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 79833840], 'label': '5878656.d.84.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.blB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BN', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278231
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 2560216252372427973, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 79833840], 'label': '5878656.d.84.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.blC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BO', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278232
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 21, 'diagramx': [1460, -1, 5117, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 17804267676843183237, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bm1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BP', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278236
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [5913, -1, 6537, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902014403666081, 711374856192144, 127314244155876453, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bp1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BS', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278237
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2476, -1, 5441, -1], 'generators': [2554923893160038643, 43545603, 25483313688004167094, 2432902008180269065, 20929016908825, 711374856192144, 376610217984000, 48530349034036445518, 27916638074998041747, 79833840, 20234124111189542545, 376784618112000], 'label': '5878656.d.84.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '84.bq1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BT', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278238
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [2270, -1, 5375, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 2560216252372427973, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 20354279938546901732, 79833840], 'label': '5878656.d.84.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.br1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BU', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278239
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [8633, -1, 7404, -1], 'generators': [2554923893160038643, 80784, 20354279938546942078, 43545603, 2432902014403666081, 711374856192144, 2560216252372427973, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bs1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BV', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278240
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6415, -1, 6697, -1], 'generators': [2554923893160038643, 43545603, 25483313688004167094, 2432902008180269065, 20929016908825, 711374856192144, 20234479798577762160, 376610217984000, 48530349034036445518, 27916638074998041747, 79833840, 376784618112000], 'label': '5878656.d.84.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '84.bt1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BW', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278241
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [6597, -1, 6754, -1], 'generators': [2554923893160038643, 43545603, 25483313688004167094, 2432902008180269065, 20929016908825, 711374856192144, 20234479798577762160, 48530349033956692558, 376610217984000, 27916638074998041747, 79833840, 376784618112000], 'label': '5878656.d.84.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.J', 'old_label': '84.bu1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BX', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 6278242
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [104, -1, 4685, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902014403666081, 711374856192144, 2560237175122399197, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.bv1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BY', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278243
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2658, -1, 5499, -1], 'generators': [2554923893160038643, 43545603, 20234124111189582840, 25483313688004167094, 2432902008180269065, 20929016908825, 711374856192144, 376610217984000, 48530349034036445518, 27916638074998041747, 79833840, 376784618112000], 'label': '5878656.d.84.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '84.bw1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.BZ', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278244
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 38540443835888000668, 80784, 43545603, 2432902008180269065, 2267882456192636, 46218736237963680475, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 79833840, 125423428146146639], 'label': '5878656.d.14.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '14.fB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.G', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278245
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [2840, -1, 5557, -1], 'generators': [2554923893160038643, 43545603, 20234124111189582840, 25483313688004167094, 2432902008180269065, 20929016908825, 711374856192144, 48530349033956692558, 376610217984000, 27916638074998041747, 79833840, 376784618112000], 'label': '5878656.d.84.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.J', 'old_label': '84.bx1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.CA', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 6278246
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [7166, -1, 6936, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902014403666081, 127335166985681277, 711374856192144, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.by1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.CB', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278247
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9920, -1, 7814, -1], 'generators': [2554923893160038643, 43545603, 25483313688004167094, 2432902008180269065, 711374856192144, 6230690184, 20922793557361, 376610217984000, 48530349034036445518, 25483736060594421365, 79833840, 376784618112000], 'label': '5878656.d.84.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '84.bz1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.CC', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278248
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 2560216252372427973, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.B', 'old_label': '84.caB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.CD', 'subgroup_fusion': None, 'weyl_group': '839808.hf'}
  • id: 6278249
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '84.caC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.CE', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278250
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [4355, -1, 6040, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902014403666081, 711374856192144, 2560216252372427973, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '84.cb1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.CF', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278251
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3797, -1, 5862, -1], 'generators': [2554923893160038643, 43545603, 25483313688004167094, 2432902008180269065, 20929016908825, 711374856192144, 20234479798577721625, 376610217984000, 48530349034036445518, 27916638074998041747, 79833840, 376784618112000], 'label': '5878656.d.84.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '84.cc1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.CG', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278252
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 112, 'diagramx': [2280, -1, 8566, -1], 'generators': [2432922937197177840, 43545603, 123912976674332013, 7807493633935922065, 376784618192784, 711374856192144, 376610217984000, 79833840, 80784, 2554923893160038643, 5065], 'label': '5878656.d.112.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.A', 'old_label': '112.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 6278253
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [104, -1, 7872, -1], 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 20356124898990222749, 376784618192784, 376610217984000, 5065, 27915859727136334324, 79833840, 23051168823283050484], 'label': '5878656.d.112.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '112.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.B', 'subgroup_fusion': None, 'weyl_group': '69984.c'}
  • id: 6278254
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [305, -1, 7936, -1], 'generators': [43545603, 23051524504484125562, 20355769211602083867, 376784618192784, 711374856192144, 376610217984000, 79833840, 80784, 2554923893160038643, 27915859727136334324, 5065], 'label': '5878656.d.112.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '112.c1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.C', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278255
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 4993830386958913679, 2432902008180269065, 711374856192144, 33169207795655724986, 6230654664, 376784618192784, 20922793521841, 376610217984000, 4867293550903701690, 2560927627228660412, 79833840], 'label': '5878656.d.14.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.B', 'old_label': '14.fC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.H', 'subgroup_fusion': None, 'weyl_group': '839808.hf'}
  • id: 6278256
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': [2462, -1, 8624, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 20922793516824, 711374856192144, 6230654664, 376784618192784, 376610217984000, 25483313406387790322, 79833840], 'label': '5878656.d.112.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '112.d1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.D', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278257
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [523, -1, 8006, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 376610217984000, 5065, 27915859727136334324, 79833840], 'label': '5878656.d.112.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '112.e1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.E', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278258
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1219, -1, 8227, -1], 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 20356124898990263043, 2556815072029303679, 376784618192784, 376610217984000, 27915859727136334324, 79833840, 23051168823283050484], 'label': '5878656.d.112.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '112.f1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.F', 'subgroup_fusion': None, 'weyl_group': '69984.c'}
  • id: 6278259
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432922937197182905, 711374856192144, 20356124898990263043, 376784618192784, 376610217984000, 27915859727136334324, 79833840, 23051168823283050484], 'label': '5878656.d.112.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '112.gB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.G', 'subgroup_fusion': None, 'weyl_group': '209952.el'}
  • id: 6278260
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432922937197182905, 40850144898997898757, 711374856192144, 35720689334021562118, 376784618192784, 376610217984000, 79833840, 33168852296738489640], 'label': '5878656.d.112.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.T', 'old_label': '112.gC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 6278261
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1594, -1, 8347, -1], 'generators': [43545603, 23173169604932874388, 25482957806137990561, 711374856192144, 376784618192784, 376610217984000, 79833840, 80784, 2554923893160038643, 17922867290603735283, 123912976674372215], 'label': '5878656.d.112.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '112.h1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.I', 'subgroup_fusion': None, 'weyl_group': '69984.hh'}
  • id: 6278262
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [123912976674332013, 25482957806137990561, 80784, 43545603, 376610217984000, 17922867290603735283, 376784618192784, 79833840, 23173169604932874388, 2554923893160038643, 711374856192144], 'label': '5878656.d.112.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '112.iB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.J', 'subgroup_fusion': None, 'weyl_group': '209952.el'}
  • id: 6278263
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 35720689334021562118, 376784618192784, 38538887984999441155, 376610217984000, 79833840, 33168852296738489640, 15367563038515846892], 'label': '5878656.d.112.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.T', 'old_label': '112.iC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.K', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 6278264
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [2634, -1, 8678, -1], 'generators': [20356124898990263043, 2432922937197177840, 43545603, 25483313406387795244, 376784618192784, 711374856192144, 376610217984000, 79833840, 80784, 2554923893160038643, 23051168823283050484], 'label': '5878656.d.112.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '112.j1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.L', 'subgroup_fusion': None, 'weyl_group': '69984.hh'}
  • id: 6278265
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1031, -1, 8168, -1], 'generators': [2432902008180269065, 43545603, 2556815072029263237, 376784618192784, 711374856192144, 376610217984000, 79833840, 7807137946547742986, 20922793521841, 2554923893160038643, 80784], 'label': '5878656.d.112.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '112.k1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.M', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278266
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 80784, 2560571939760647732, 43545603, 4993830386958913679, 2432902008180269065, 711374856192144, 33169207795655724986, 6230654664, 376784618192784, 20922793521841, 376610217984000, 4867293550903701690, 79833840], 'label': '5878656.d.14.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.B', 'old_label': '14.gB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.I', 'subgroup_fusion': None, 'weyl_group': '839808.hf'}
  • id: 6278267
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [872, -1, 8117, -1], 'generators': [43545603, 23172813923731799066, 25482957806137990561, 376784618192784, 2556815072029263237, 711374856192144, 376610217984000, 79833840, 80784, 2554923893160038643, 17923222977991874165], 'label': '5878656.d.112.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '112.l1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.N', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278268
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 20356124898990263043, 376784618192784, 2556815072029263237, 376610217984000, 27915859727136334324, 79833840, 23051168823283050484], 'label': '5878656.d.112.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '112.mB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.O', 'subgroup_fusion': None, 'weyl_group': '23328.p'}
  • id: 6278269
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 15367207351127667812, 711374856192144, 33287787238666671092, 376784618192784, 38538887984999441155, 376610217984000, 35602444756981474080, 79833840], 'label': '5878656.d.112.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.T', 'old_label': '112.mC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.P', 'subgroup_fusion': None, 'weyl_group': '20000.de'}
  • id: 6278270
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1940, -1, 8457, -1], 'generators': [2554923893160038643, 80784, 43545603, 23051524504484125562, 711374856192144, 376784618192784, 25483313406387795244, 376610217984000, 20355769211602043525, 2432922937197177840, 79833840], 'label': '5878656.d.112.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '112.n1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.Q', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278271
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 56, 'diagramx': [713, -1, 8066, -1], 'generators': [2432922937197177840, 43545603, 17923222890853539869, 25483313406387795244, 376784618192784, 711374856192144, 376610217984000, 79833840, 80784, 2554923893160038643, 23173169611119938044], 'label': '5878656.d.112.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.F', 'old_label': '112.o1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.R', 'subgroup_fusion': None, 'weyl_group': '104976.cb'}
  • id: 6278272
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1406, -1, 8287, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 7807137946547742986, 2556815072029303679, 376784618192784, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.112.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '112.p1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.S', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278273
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [2098, -1, 8508, -1], 'generators': [2554923893160038643, 2556835907640860159, 80784, 43545603, 2432902008180269065, 7807137946547742986, 711374856192144, 376784618192784, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.112.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '112.q1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.T', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278274
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [2963, -1, 8783, -1], 'generators': [2432902008180269065, 43545603, 376784618192784, 711374856192144, 376610217984000, 79833840, 7807137946547742986, 2556835907640900357, 20922793521841, 2554923893160038643, 80784], 'label': '5878656.d.112.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '112.r1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.U', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278275
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1781, -1, 8407, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 20922793521841, 25483313406387795244, 376610217984000, 79833840], 'label': '5878656.d.112.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '112.s1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.V', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278276
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 23051524504484125562, 2432922937197182905, 711374856192144, 376784618192784, 376610217984000, 20355769211602043525, 27915859727136334324, 79833840], 'label': '5878656.d.112.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '112.tB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.W', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278277
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 38540443835888000668, 80784, 43545603, 2432902008180269065, 46218736237963680475, 711374856192144, 6230654664, 376784618192784, 20922793521841, 2267882456187478, 376610217984000, 79833840, 125423428146146639], 'label': '5878656.d.14.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '14.gC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.J', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278278
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432922937197182905, 40850144898997898757, 711374856192144, 376784618192784, 376610217984000, 35720333559415175036, 79833840, 33168831373952230560], 'label': '5878656.d.112.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.Y', 'old_label': '112.tC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.X', 'subgroup_fusion': None, 'weyl_group': '104976.cd'}
  • id: 6278279
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [43545603, 2556815072029303679, 23172813923731799066, 25482957806137990561, 711374856192144, 376784618192784, 376610217984000, 79833840, 80784, 2554923893160038643, 17923222977991874165], 'label': '5878656.d.112.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '112.uB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.Y', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278280
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 376784618192784, 38538887984999441155, 15367207351127662654, 35602465685998382761, 376610217984000, 35720333559415175036, 79833840], 'label': '5878656.d.112.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.Y', 'old_label': '112.uC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.Z', 'subgroup_fusion': None, 'weyl_group': '34992.r'}
  • id: 6278281
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [2804, -1, 8733, -1], 'generators': [2554923893160038643, 80784, 43545603, 23051524504484125562, 711374856192144, 376784618192784, 376610217984000, 123912976674332013, 20355769211602043525, 27915859727136334324, 79833840], 'label': '5878656.d.112.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '112.v1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.BA', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278282
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 23051524504484125562, 711374856192144, 376784618192784, 123912976674372215, 376610217984000, 20355769211602043525, 27915859727136334324, 79833840], 'label': '5878656.d.112.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '112.wB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.BB', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278283
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '112.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [2554923893160038643, 33287431638416866414, 15367563038515841974, 80784, 43545603, 711374856192144, 376784618192784, 38538887984999441155, 376610217984000, 33168831380175622561, 79833840], 'label': '5878656.d.112.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.Y', 'old_label': '112.wC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.BC', 'subgroup_fusion': None, 'weyl_group': '104976.cd'}
  • id: 6278284
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [2875, -1, 9721, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 2432902014403666081, 2432902008260107584, 711374856192144, 4992341032952254205, 376784574647040, 6025588999390655, 376610217984000, 33165786538091451331, 243], 'label': '5878656.d.126.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.A', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278285
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [3286, -1, 9852, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 2432902014403666081, 6381363605818175, 2432902008260107584, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 33165786538091451331, 243], 'label': '5878656.d.126.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.B', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278286
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [2681, -1, 9659, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 2432902014403666081, 2432902008260107584, 711374856192144, 4992341032952254205, 376784574647040, 6025588999390655, 376610217984000, 243, 35598688459089800155], 'label': '5878656.d.126.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.c1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.C', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278287
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [104, -1, 8838, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 2432902014403666081, 6381363605818175, 2432902008260107584, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 243, 35598688459089800155], 'label': '5878656.d.126.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.d1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.D', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278288
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '16.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 8, 'diagramx': [502, -1, 825, -1], 'generators': [2554923893160038643, 80784, 43545603, 711374856192144, 33167719199644704594, 376784618192784, 376610217984000, 4865804298049909800, 79833840], 'label': '5878656.d.16.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '16.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.A', 'subgroup_fusion': None, 'weyl_group': '244944.a'}
  • id: 6278289
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [3480, -1, 9914, -1], 'generators': [35599065162713141759, 122356562443320245, 43545603, 122356568673969844, 711374856192144, 4992006268393879805, 122377491460229068, 376610217984000, 2560217097255264475, 2554923893160119043, 79833840, 376784618112000], 'label': '5878656.d.126.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.E', 'old_label': '126.e1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.E', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 6278290
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [320, -1, 8907, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 2432902014403666081, 6381363605818175, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 33165786538091451331, 5065, 243], 'label': '5878656.d.126.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.f1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.F', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278291
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [1573, -1, 9306, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 2432902014403666081, 2438927597092608575, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 33165786538091451331, 5065, 243], 'label': '5878656.d.126.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.g1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.G', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278292
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [1073, -1, 9146, -1], 'generators': [2432922930966533304, 2554923893160038643, 6381444477254975, 33165786450829738171, 80784, 2432902014403666081, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 243, 5065], 'label': '5878656.d.126.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.h1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.H', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278293
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1323, -1, 9226, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 33165786450829738171, 2432902014403666081, 2438927597092608575, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 243, 5065], 'label': '5878656.d.126.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '126.i1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.I', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278294
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [3080, -1, 9787, -1], 'generators': [2554923893160038643, 80784, 33169985768766314405, 2432902008180269065, 711374856192144, 6230654664, 4992341032952254205, 376784574647040, 20922793521841, 376610217984000, 243, 5065], 'label': '5878656.d.126.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.j1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.J', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278295
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2486, -1, 9597, -1], 'generators': [2554923893160038643, 80784, 6310488504, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 33165786538091451331, 5065, 243, 20922873355681, 2432902008260102521], 'label': '5878656.d.126.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '126.k1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.K', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278296
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [2292, -1, 9536, -1], 'generators': [2554923893160038643, 6381444477254975, 80784, 2432902008180269065, 711374856192144, 6230654664, 4992341032952254205, 376784574647040, 20922793521841, 376610217984000, 243, 5065], 'label': '5878656.d.126.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.l1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.L', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278297
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [822, -1, 9066, -1], 'generators': [2554923893160038643, 80784, 6381363605818175, 711374856192144, 6310488504, 4992341032952254205, 376784574647040, 376610217984000, 243, 35598688459089800155, 20922873355681, 2432902008260102521], 'label': '5878656.d.126.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.m1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.M', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278298
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [1824, -1, 9386, -1], 'generators': [2554923893160038643, 80784, 711374856192144, 6310488504, 4992341032952254205, 376784574647040, 6025588999390655, 376610217984000, 243, 35598688459089800155, 20922873355681, 2432902008260102521], 'label': '5878656.d.126.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.n1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.N', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278299
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '16.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 8, 'diagramx': [99, -1, 696, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 50968584844915144585, 6230654664, 376784618192784, 20922793521841, 376610217984000, 79833840, 28040551045668610290], 'label': '5878656.d.16.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.A', 'old_label': '16.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.B', 'subgroup_fusion': None, 'weyl_group': '734832.a'}
  • id: 6278300
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [571, -1, 8987, -1], 'generators': [2554923893160038643, 80784, 6381363605818175, 6310488504, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 33165786538091451331, 243, 20922873355681, 2432902008260102521], 'label': '5878656.d.126.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.o1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.O', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278301
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '126.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [2075, -1, 9466, -1], 'generators': [2554923893160038643, 80784, 6310488504, 711374856192144, 4992341032952254205, 376784574647040, 6025588999390655, 376610217984000, 33165786538091451331, 243, 20922873355681, 2432902008260102521], 'label': '5878656.d.126.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '126.p1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.P', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278302
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 64, 'diagramx': [107, -1, 9973, -1], 'generators': [2554923893160038643, 80784, 43545603, 7686961927760061836, 711374856192144, 376784618192784, 376610217984000, 20234501653768312563, 79833840], 'label': '5878656.d.128.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1', 'old_label': '128.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '30618.d'}
  • id: 6278303
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '168.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5878656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4814, -1, 5457], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.168.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '168.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '168.a1.N', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.A', 'subgroup_fusion': None, 'weyl_group': '5878656.d'}
  • id: 6278304
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '336.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5878656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4814, -1, 6780], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.336.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '336.a1.N', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.A', 'subgroup_fusion': None, 'weyl_group': '5878656.d'}
  • id: 6278305
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '896.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 112, 'diagramx': None, 'generators': [711374856192000, 12551631720495794164, 4866515391289305600, 45360, 4, 45604, 10240039954764219024, 43545600], 'label': '5878656.d.896.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.A', 'old_label': '896.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '896.a1', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
  • id: 6278306
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '1344.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5878656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4332, -1, 8005], 'generators': [43545603, 2432922937197182905, 376784618192784, 711374856192144, 376610217984000, 79833840, 80784, 2554923893160038643], 'label': '5878656.d.1344.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1344.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1344.a1.N', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.A', 'subgroup_fusion': None, 'weyl_group': '5878656.d'}
  • id: 6278307
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '2187.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 2187, 'diagramx': None, 'generators': [456053212104, 2432902008260102521, 40852813574407667763, 20922873436081, 85801, 87261839400], 'label': '5878656.d.2187.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2187.A', 'old_label': '2187.a1.M', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2187.A', 'subgroup_fusion': None, 'weyl_group': '1344.11686'}
  • id: 6278308
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '2688.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2688.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3906, -1, 8973], 'generators': [80784, 43545603, 376610217984000, 376784618192784, 79833840, 2554923893160038643, 711374856192144], 'label': '5878656.d.2688.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2688.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2688.a1.N', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2688.A', 'subgroup_fusion': None, 'weyl_group': '57600.bx'}
  • id: 6278309
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '45927.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 45927, 'diagramx': None, 'generators': [2439303362435094214, 355693655116825, 2439304207310516854, 2267789007329730, 2438947668779982454, 2433257695604736001, 2432902008216561840], 'label': '5878656.d.45927.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45927.a1', 'old_label': '45927.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45927.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 6278310
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [163, 6747, 128, 3570], 'generators': [2554923893160038643, 80784, 43545603, 48531838100003591756, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 79833840, 124624921378452029], 'label': '5878656.d.2.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '5878656.d'}
  • id: 6278311
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '16.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 8, 'diagramx': [285, -1, 756, -1], 'generators': [4987470321248705520, 43545603, 376610217984000, 711374856192144, 376784618192784, 79833840, 80784, 2554923893160038643, 33167698364033107772], 'label': '5878656.d.16.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '16.c1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.C', 'subgroup_fusion': None, 'weyl_group': '734832.c'}
  • id: 6278312
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '839808.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 46656, 'diagramx': None, 'generators': [20353523834860634883], 'label': '5878656.d.839808.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '839808.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '839808.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 6278313
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '5878656.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3253, -1, 9734], 'generators': [], 'label': '5878656.d.5878656.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5878656.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5878656.a1.N', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5878656.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 6278314
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '21.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '21T136', 'count': 21, 'diagramx': [138, -1, 897, -1], 'generators': [2554923893160038643, 80784, 2559794631252480245, 6310488504, 711374856192144, 376784574647040, 123511158042497039, 376610217984000, 5065, 243, 48651639003880721157, 33169208158606625401, 20922873355681, 2432902008260102521], 'label': '5878656.d.21.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '21.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.A', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278315
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '21.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 21, 'diagramx': [361, -1, 969, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 2559459866694105845, 711374856192144, 6230654664, 376784618192784, 20922793521841, 123511158042497039, 376610217984000, 5065, 33169208158606625401, 79833840], 'label': '5878656.d.21.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '21.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.B', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278316
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '24.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 8, 'diagramx': [99, -1, 1027, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 40972547511473535935, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.24.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.A', 'old_label': '24.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.A', 'subgroup_fusion': None, 'weyl_group': '734832.a'}
  • id: 6278317
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '24.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '24T23418', 'count': 24, 'diagramx': [304, -1, 1092, -1], 'generators': [50965894790950325306, 376610261529603, 711549256400784, 4987804984777445162, 2554547282942054643, 376610217984144, 79833840, 122377860295303921, 711374856272784], 'label': '5878656.d.24.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.B', 'old_label': '24.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.B', 'subgroup_fusion': None, 'weyl_group': '244944.a'}
  • id: 6278318
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1636, -1, 1648, -1], 'generators': [2554923893160038643, 80784, 43545603, 46220246608177474435, 2432902008180269065, 20929016913840, 711374856192144, 23173592158545517315, 23171324569804863234, 376784618192784, 2554547852782039108, 376610217984000, 79833840], 'label': '5878656.d.28.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '28.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.A', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278319
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': [952, -1, 1429, -1], 'generators': [2554923893160038643, 80784, 43545603, 46220602295609199355, 2432902008180269065, 23051946970958394235, 20929016913840, 711374856192144, 376784618192784, 2554547852782039108, 23171324569804858315, 376610217984000, 79833840], 'label': '5878656.d.28.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '28.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.B', 'subgroup_fusion': None, 'weyl_group': '209952.el'}
  • id: 6278320
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 7, 'diagramx': [327, -1, 1230, -1], 'generators': [2554923893160038643, 6045753968697474, 80784, 43545603, 2554547953847840884, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 79833840, 126557744650721999, 2432902008180274080], 'label': '5878656.d.28.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '28.c1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.C', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278321
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 7, 'diagramx': [127, -1, 1167, -1], 'generators': [2554923893160038643, 80784, 43545603, 2554547953847840884, 711374856192144, 6230654664, 2559083055431086679, 6401441436710394, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.28.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '28.d1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.D', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278322
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1883, -1, 1727, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 2556392612177254564, 376784618192784, 20922793521841, 376610217984000, 5065, 456053212104, 79833840], 'label': '5878656.d.28.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '28.e1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.E', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278323
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '7.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 15367563038515841974, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 30736306063171865547, 376784618192784, 20922793521841, 33287452567433775092, 376610217984000, 5065, 79833840, 10243776550150115038], 'label': '5878656.d.7.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '7.aB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.A', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278324
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 7, 'diagramx': [740, -1, 1362, -1], 'generators': [2554923893160038643, 80784, 6045753968697474, 43545603, 2554547953847840884, 711374856192144, 6230654664, 2559083055431086679, 376784618192784, 456053207041, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.28.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '28.f1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.F', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278325
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 7, 'diagramx': [1161, -1, 1496, -1], 'generators': [2554923893160038643, 80784, 6045753968697474, 43545603, 2554547953847840884, 711374856192144, 6230654664, 2432902377051641520, 2559083055431086679, 376784618192784, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.28.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '28.g1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.G', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278326
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 7, 'diagramx': [525, -1, 1294, -1], 'generators': [2554923893160038643, 80784, 6045753968697474, 43545603, 2554547953847840884, 711374856192144, 6230654664, 2559083055431086679, 2432902377051636505, 376784618192784, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.28.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '28.h1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.H', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278327
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 80784, 46220246608177474435, 43545603, 2432902008180269065, 711374856192144, 23173592158545517315, 6230654664, 376784618192784, 20922793521841, 23171324569804858315, 376610217984000, 79833840], 'label': '5878656.d.28.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.B', 'old_label': '28.iB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.I', 'subgroup_fusion': None, 'weyl_group': '839808.hf'}
  • id: 6278328
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 80784, 6045753968697474, 43545603, 2432902008180269065, 2554547953847840884, 711374856192144, 6230654664, 126913344900531839, 376784618192784, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.28.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '28.iC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.J', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278329
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '28.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 7, 'diagramx': [1376, -1, 1565, -1], 'generators': [2554923893160038643, 80784, 6045753968697474, 43545603, 2554547953847840884, 711374856192144, 6230654664, 2559083055431086679, 376784618192784, 20922793521841, 376610217984000, 456053212104, 79833840], 'label': '5878656.d.28.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '28.j1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.K', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278330
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '42T2491', 'count': 21, 'diagramx': [784, -1, 2001, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 2432902014403666081, 2432902008260107584, 711374856192144, 4992341032952254205, 376784574647040, 46097824112073556318, 376610217984000, 2434035849031987795, 30857595563327299227, 243], 'label': '5878656.d.42.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '42.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.A', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278331
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '42T2489', 'count': 21, 'diagramx': [600, -1, 1943, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 2432902014403666081, 2432902008260107584, 711374856192144, 4992341032952254205, 376784574647040, 46097824112073556318, 2434035849031992957, 376610217984000, 30857595563327299227, 243], 'label': '5878656.d.42.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '42.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.B', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278332
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 21, 'diagramx': [978, -1, 2063, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 2432902014403666081, 43545603, 4992006268393879805, 711374856192144, 376784618192784, 2434035849075533396, 376610217984000, 30736306150426396829, 79833840, 2432902008180274080], 'label': '5878656.d.42.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.c1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.C', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278333
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 21, 'diagramx': [2190, -1, 2449, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 2432902014403666081, 4992006268393879805, 711374856192144, 376784618192784, 2434035849075538558, 376610217984000, 30736306150426396829, 79833840, 2432902008180274080], 'label': '5878656.d.42.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.d1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.D', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278334
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '7.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 25604937946574386414, 6230654664, 40851679545216368784, 376784618192784, 51086385778026395516, 20922793521841, 48652772006139834931, 376610217984000, 5065, 79833840], 'label': '5878656.d.7.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.B', 'old_label': '7.aC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.B', 'subgroup_fusion': None, 'weyl_group': '839808.hf'}
  • id: 6278335
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 21, 'diagramx': [2782, -1, 2638, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 2432902014403666081, 4992006268393879805, 711374856192144, 30858306938263324827, 376784618192784, 2434035849075533396, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.42.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.e1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.E', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278336
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 21, 'diagramx': [2600, -1, 2580, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 4992006268393879805, 30858306938263324827, 376784618192784, 2434035849075538558, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.42.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.f1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.F', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278337
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [3617, -1, 2904, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 4992006268393879805, 30736285227596551707, 376784618192784, 376610217984000, 1133840938810317, 5065, 79833840], 'label': '5878656.d.42.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.g1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.G', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278338
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [383, -1, 1874, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 4992006268393879805, 30736285227596551707, 376784618192784, 2434035849075533396, 376610217984000, 5065, 79833840], 'label': '5878656.d.42.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.h1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.H', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278339
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '42T2487', 'count': 21, 'diagramx': [1812, -1, 2329, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 30736640914984771229, 2432902014403666081, 46219448376787329118, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 1133840938810317, 243, 5065], 'label': '5878656.d.42.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '42.i1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.I', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278340
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '42T2509', 'count': 42, 'diagramx': [1996, -1, 2388, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 30736640914984771229, 2432902014403666081, 46219448457782145118, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 1133840938810317, 243, 5065], 'label': '5878656.d.42.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.J', 'old_label': '42.j1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.J', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 6278341
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [1412, -1, 2202, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 2432902014403666081, 711374856192144, 4992006268393879805, 376784618192784, 376610217984000, 1133840938810317, 30736306150426396829, 5065, 79833840], 'label': '5878656.d.42.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.k1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.K', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278342
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 21, 'diagramx': [138, -1, 1795, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 2432902014403666081, 4992006268393879805, 711374856192144, 376784618192784, 2434035849075533396, 376610217984000, 30736306150426396829, 5065, 79833840], 'label': '5878656.d.42.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.l1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.L', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278343
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '42T2493', 'count': 7, 'diagramx': [3216, -1, 2776, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 30736640914984771229, 2432902014403666081, 46219448376787329118, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 2434035849031987795, 5065, 243], 'label': '5878656.d.42.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '42.m1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.M', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278344
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '42T2488', 'count': 21, 'diagramx': [2400, -1, 2517, -1], 'generators': [2554923893160038643, 80784, 30736640914984771229, 6310488504, 711374856192144, 4992341032952254205, 376784574647040, 46097824112073556318, 376610217984000, 243, 5065, 20922873355681, 2432902008260102521], 'label': '5878656.d.42.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '42.n1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.N', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278345
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '8.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 8, 'diagramx': [599, -1, 357, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 38538176784579745655, 711374856192144, 6230654664, 376784618192784, 38420623222608394923, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.8.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.A', 'old_label': '8.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.A', 'subgroup_fusion': None, 'weyl_group': '734832.a'}
  • id: 6278346
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 21, 'diagramx': [1183, -1, 2129, -1], 'generators': [2554923893160038643, 30856039712562194637, 80784, 43545603, 2432902008180269065, 4992006268393879805, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.42.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.o1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.O', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278347
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 4992006268393879805, 711374856192144, 6230654664, 376784618192784, 2434035849075533396, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.42.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.B', 'old_label': '42.pB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.P', 'subgroup_fusion': None, 'weyl_group': '839808.hf'}
  • id: 6278348
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 4992006268393879805, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 30736306150426396829, 5065, 79833840], 'label': '5878656.d.42.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '42.pC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.Q', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278349
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 21, 'diagramx': [3867, -1, 2984, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 4992006268393879805, 711374856192144, 6230654664, 376784618192784, 2434035849075533396, 20922793521841, 376610217984000, 30736306150426396829, 79833840], 'label': '5878656.d.42.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.q1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.R', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278350
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '42T2490', 'count': 21, 'diagramx': [1629, -1, 2271, -1], 'generators': [2554923893160038643, 80784, 46219469206255367494, 6310488504, 711374856192144, 4992341032952254205, 376784574647040, 376610217984000, 2434035849031987795, 243, 30857595563327299227, 20922873355681, 2432902008260102521], 'label': '5878656.d.42.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '42.r1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.S', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278351
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 4992006268393879805, 711374856192144, 6230654664, 30858306938263324827, 376784618192784, 2434035849075533396, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.42.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.sB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.T', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278352
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 4992006268393879805, 711374856192144, 6230654664, 376784618192784, 2434035849075538558, 20922793521841, 376610217984000, 30736306150426396829, 79833840], 'label': '5878656.d.42.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.sC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.U', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278353
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 21, 'diagramx': [2998, -1, 2707, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 4992006268393879805, 711374856192144, 6230654664, 30858306938263324827, 376784618192784, 2434035849075538558, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.42.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.B', 'old_label': '42.t1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.V', 'subgroup_fusion': None, 'weyl_group': '279936.z'}
  • id: 6278354
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '42.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': '42T2492', 'count': 21, 'diagramx': [3398, -1, 2835, -1], 'generators': [2554923893160038643, 80784, 46219469206255367494, 6310488504, 711374856192144, 4992341032952254205, 376784574647040, 2434035849031992957, 376610217984000, 243, 30857595563327299227, 20922873355681, 2432902008260102521], 'label': '5878656.d.42.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '42.u1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.W', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278355
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '48.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [251, -1, 3098, -1], 'generators': [2554923893239872147, 376784654480880, 456053212104, 79914240, 376610297817840, 48656550071464519108, 243, 711374936025600], 'label': '5878656.d.48.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '48.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.A', 'subgroup_fusion': None, 'weyl_group': '244944.a'}
  • id: 6278356
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '8.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 8, 'diagramx': [394, -1, 292, -1], 'generators': [2554923893160038643, 80784, 4866181001709574348, 43545603, 2432922937197182905, 711374856192144, 376784618192784, 17802711718870032597, 376610217984000, 79833840], 'label': '5878656.d.8.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '8.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.B', 'subgroup_fusion': None, 'weyl_group': '734832.b'}
  • id: 6278357
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '48.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 8, 'diagramx': [80, -1, 3044, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 27919261827122842923, 376784618192784, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.48.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.A', 'old_label': '48.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.B', 'subgroup_fusion': None, 'weyl_group': '734832.a'}
  • id: 6278358
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1991, -1, 3762, -1], 'generators': [2554923893160038643, 123155464387420559, 35719977590154363594, 80784, 43545603, 23173190708349875881, 126202258191380524, 711374856192144, 376784618192784, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.56.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '56.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.A', 'subgroup_fusion': None, 'weyl_group': '209952.el'}
  • id: 6278359
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': [3946, -1, 4385, -1], 'generators': [2554923893160038643, 80784, 43545603, 126181422579783842, 35719998600122502474, 20929016908825, 711374856192144, 376784618192784, 123511158042537333, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.56.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '56.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.B', 'subgroup_fusion': None, 'weyl_group': '209952.el'}
  • id: 6278360
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1411, -1, 3577, -1], 'generators': [2554923893160038643, 80784, 35719977590154363594, 43545603, 23173190708349916320, 711374856192144, 376784618192784, 123511158042497039, 376610217984000, 79833840, 126181335397863844, 2432902008180274080], 'label': '5878656.d.56.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '56.c1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.C', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278361
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [3545, -1, 4257, -1], 'generators': [2554923893160038643, 80784, 33287075669156014674, 43545603, 126202258191380524, 23173190708349916320, 711374856192144, 376784618192784, 123511158042537333, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.56.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '56.d1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.D', 'subgroup_fusion': None, 'weyl_group': '69984.c'}
  • id: 6278362
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': [4128, -1, 4443, -1], 'generators': [2554923893160038643, 80784, 43545603, 35719998600122502474, 20929016908825, 711374856192144, 376784618192784, 123511158042497039, 376610217984000, 126202345366042922, 79833840, 2432902008180274080], 'label': '5878656.d.56.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '56.e1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.E', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278363
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 56, 'diagramx': [1819, -1, 3707, -1], 'generators': [2554923893160038643, 126181335397858682, 80784, 43545603, 123511151775599735, 35719998600122502474, 20929016908825, 711374856192144, 376784618192784, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.56.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.F', 'old_label': '56.f1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.F', 'subgroup_fusion': None, 'weyl_group': '104976.cb'}
  • id: 6278364
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [2209, -1, 3831, -1], 'generators': [2554923893160038643, 80784, 33287075669156014674, 43545603, 23173190708349875881, 711374856192144, 376784618192784, 376610217984000, 79833840, 123155464387380213, 126181335397863844, 2432902008180274080], 'label': '5878656.d.56.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '56.g1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.G', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278365
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': [551, -1, 3303, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 376784618192784, 376610217984000, 17922532438703738161, 5065, 79833840, 15367986068087767227], 'label': '5878656.d.56.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '56.h1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.H', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278366
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': [3775, -1, 4330, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 376784618192784, 376610217984000, 17922511603092141624, 5065, 79833840, 15367986068087767227], 'label': '5878656.d.56.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '56.i1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.I', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278367
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '8.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 8, 'diagramx': [143, -1, 212, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432922937197182905, 711374856192144, 376784618192784, 4866181088847948746, 376610217984000, 79833840, 20235258039618576599], 'label': '5878656.d.8.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '8.c1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.C', 'subgroup_fusion': None, 'weyl_group': '734832.c'}
  • id: 6278368
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1629, -1, 3646, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 376784618192784, 15367965058155870987, 376610217984000, 17922511603092141624, 79833840, 2432902008180274080], 'label': '5878656.d.56.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '56.j1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.J', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278369
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [2462, -1, 3912, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 17922511603092181825, 376784618192784, 15367965058155870987, 376610217984000, 79833840, 2432902008180274080], 'label': '5878656.d.56.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '56.k1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.K', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278370
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '168.A', 'coset_action_label': None, 'count': 28, 'diagramx': [4309, -1, 4501, -1], 'generators': [2554923893160038643, 80784, 25605737136614821707, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.56.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '56.l1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.L', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278371
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': [3301, -1, 4179, -1], 'generators': [2554923893160038643, 80784, 43545603, 23173190708349875881, 126202258191380524, 2432922937197182905, 711374856192144, 376784618192784, 123511158042537333, 376610217984000, 79833840, 33287075669155974475], 'label': '5878656.d.56.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '56.m1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.M', 'subgroup_fusion': None, 'weyl_group': '209952.el'}
  • id: 6278372
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [2681, -1, 3982, -1], 'generators': [2554923893160038643, 80784, 43545603, 2559794805608982002, 23173190708349916320, 2556413166179220210, 20929016908825, 711374856192144, 376784618192784, 376610217984000, 33287096510991003594, 79833840], 'label': '5878656.d.56.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '56.n1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.N', 'subgroup_fusion': None, 'weyl_group': '209952.el'}
  • id: 6278373
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [2881, -1, 4046, -1], 'generators': [2554923893160038643, 80784, 43545603, 23173190708349875881, 20929016908825, 711374856192144, 376784618192784, 123511158042497039, 376610217984000, 33287096510991003594, 79833840, 126181335397863844], 'label': '5878656.d.56.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '56.o1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.O', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278374
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 7, 'diagramx': [121, -1, 3166, -1], 'generators': [2432922930966533304, 2554923893160038643, 80784, 43545603, 711374856192144, 6230654664, 28038639144831418827, 376784618192784, 376610217984000, 10238107386324873000, 2555258939494911624, 79833840], 'label': '5878656.d.56.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '56.p1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.P', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278375
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 28, 'diagramx': [3101, -1, 4115, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 17922511603092181825, 376784618192784, 15367965145294245389, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.56.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '56.q1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.Q', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278376
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': [333, -1, 3233, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432922937197182905, 711374856192144, 376784618192784, 123511158042497039, 376610217984000, 126202345366042922, 23172834933743529001, 79833840, 33287075669155974475], 'label': '5878656.d.56.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '56.r1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.R', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278377
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [2554923893160038643, 123155464387420559, 80784, 43545603, 126202258191380524, 2432922937197182905, 35719998600122502474, 711374856192144, 376784618192784, 376610217984000, 23172834933743529001, 79833840], 'label': '5878656.d.56.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '56.sB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.S', 'subgroup_fusion': None, 'weyl_group': '209952.el'}
  • id: 6278378
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 7, 'diagramx': [121, -1, 415, -1], 'generators': [2554923893160038643, 38540443835888000668, 80784, 43545603, 2432902008180269065, 2267882456192636, 46218736237963680475, 711374856192144, 6230649601, 376784618192784, 20922793521841, 376610217984000, 79833840, 125423428146146639], 'label': '5878656.d.14.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '14.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.A', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278379
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [2554923893160038643, 80784, 25606092817815937227, 43545603, 10238107299150210601, 2432922937197182905, 711374856192144, 376784618192784, 17922532525885658304, 376610217984000, 2555258939494911624, 79833840], 'label': '5878656.d.56.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.T', 'old_label': '56.sC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.T', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 6278380
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [792, -1, 3380, -1], 'generators': [2554923893160038643, 80784, 33287096504767571154, 43545603, 23173190708349875881, 2559794805608982002, 2556413166179220210, 20929016908825, 711374856192144, 376784618192784, 376610217984000, 79833840], 'label': '5878656.d.56.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.B', 'old_label': '56.t1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.U', 'subgroup_fusion': None, 'weyl_group': '69984.hh'}
  • id: 6278381
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1033, -1, 3456, -1], 'generators': [2554923893160038643, 80784, 33287096504767571154, 43545603, 23173190708349916320, 20929016908825, 711374856192144, 376784618192784, 123511158042497039, 376610217984000, 79833840, 126181335397863844], 'label': '5878656.d.56.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '56.u1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.V', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278382
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '336.A', 'coset_action_label': None, 'count': 28, 'diagramx': [1222, -1, 3517, -1], 'generators': [2554923893160038643, 80784, 43545603, 2432902008180269065, 711374856192144, 6230654664, 376784618192784, 15367965145294245389, 20922793521841, 376610217984000, 17922511603092141624, 79833840], 'label': '5878656.d.56.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.E', 'old_label': '56.v1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.W', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278383
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [2554923893160038643, 80784, 43545603, 23173190708349875881, 2432922937197182905, 35719998600122502474, 711374856192144, 376784618192784, 376610217984000, 126202345366042922, 79833840, 123155464387380213], 'label': '5878656.d.56.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.A', 'old_label': '56.wB', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.X', 'subgroup_fusion': None, 'weyl_group': '209952.df'}
  • id: 6278384
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '56.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [2554923893160038643, 80784, 25606092817815937227, 43545603, 2432922937197182905, 711374856192144, 376784618192784, 376610217984000, 17922511603092141624, 10238107386324873000, 2555258939494951825, 79833840], 'label': '5878656.d.56.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.Y', 'old_label': '56.wC', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.Y', 'subgroup_fusion': None, 'weyl_group': '104976.cd'}
  • id: 6278385
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '63.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [115, -1, 4563, -1], 'generators': [33290497490592625948, 2432902008216556825, 2554923893160038643, 80784, 30854550559297092355, 6266942760, 20922829809985, 711374856192144, 376784574647040, 376610217984000, 5065, 243, 15366830828048058117], 'label': '5878656.d.63.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1', 'old_label': '63.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '63.a1', 'subgroup_fusion': None, 'weyl_group': '93312.bs'}
  • id: 6278386
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 64, 'diagramx': [107, -1, 4626, -1], 'generators': [40969521815299776570, 43545603, 2432922937197182905, 376784618192784, 711374856192144, 376610217984000, 79833840, 80784, 2554923893160038643, 15491455481536553764], 'label': '5878656.d.64.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1', 'old_label': '64.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '91854.c'}
  • id: 6278387
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [7395, -1, 7009, -1], 'generators': [2554923893160038643, 20354279944770293494, 15489631443958905145, 43545603, 79914240, 2560216252372427973, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 2432902014447206424, 711374936025600], 'label': '5878656.d.84.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.A', 'old_label': '84.a1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.A', 'subgroup_fusion': None, 'weyl_group': '69984.hh'}
  • id: 6278388
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 42, 'diagramx': [5459, -1, 6392, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 2432902014403661064, 43545603, 127335166985681277, 711374856192144, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.E', 'old_label': '84.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.B', 'subgroup_fusion': None, 'weyl_group': '139968.ca'}
  • id: 6278389
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '14.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 7, 'diagramx': [821, -1, 638, -1], 'generators': [2554923893160038643, 38540443835888000668, 80784, 43545603, 2432902008180269065, 46218736237963680475, 711374856192144, 6230649601, 376784618192784, 20922793521841, 2267882456187478, 376610217984000, 79833840, 125423428146146639], 'label': '5878656.d.14.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.A', 'old_label': '14.b1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.B', 'subgroup_fusion': None, 'weyl_group': '839808.hh'}
  • id: 6278390
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 42, 'diagramx': [1061, -1, 4990, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902014403661064, 711374856192144, 127314244155876453, 376784618192784, 124268757511323333, 20922793521841, 376610217984000, 79833840], 'label': '5878656.d.84.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.E', 'old_label': '84.c1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.C', 'subgroup_fusion': None, 'weyl_group': '139968.ca'}
  • id: 6278391
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 42, 'diagramx': [1654, -1, 5179, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 2432902014403661064, 43545603, 711374856192144, 2560237175122399197, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 79833840], 'label': '5878656.d.84.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.F', 'old_label': '84.d1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.D', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 6278392
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [9192, -1, 7582, -1], 'generators': [15489986956990501921, 127314244155911493, 124268757511323333, 2432902014403661064, 711374936025600, 2554923893160038643, 376784654480880, 43626480, 376610261529744, 20354279944770293494, 20922829809985, 79833747], 'label': '5878656.d.84.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.E', 'old_label': '84.e1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.E', 'subgroup_fusion': None, 'weyl_group': '69984.b'}
  • id: 6278393
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9010, -1, 7524, -1], 'generators': [2554923893160038643, 43545603, 25483313688004167094, 2432902008180269065, 20929016908825, 711374856192144, 27916617145981132829, 376610217984000, 48530349034036445518, 5065, 79833840, 376784618112000], 'label': '5878656.d.84.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.A', 'old_label': '84.f1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.F', 'subgroup_fusion': None, 'weyl_group': '279936.f'}
  • id: 6278394
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1344.A', 'coset_action_label': None, 'count': 42, 'diagramx': [8107, -1, 7236, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 2432902014403661064, 711374856192144, 2560216252372427973, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 79833840], 'label': '5878656.d.84.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.F', 'old_label': '84.g1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.G', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 6278395
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5878656.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [6172, -1, 6619, -1], 'generators': [2554923893160038643, 20354279944770293494, 43545603, 2432902014403661064, 79914240, 20922829809985, 376784618192784, 124268757511328399, 376610297817840, 15490342737863826745, 711374899737840, 2560216252372508853], 'label': '5878656.d.84.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.H', 'old_label': '84.h1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.H', 'subgroup_fusion': None, 'weyl_group': '69984.c'}
  • id: 6278396
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 42, 'diagramx': [3615, -1, 5804, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 711374856192144, 2560216339510807437, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.E', 'old_label': '84.i1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.I', 'subgroup_fusion': None, 'weyl_group': '139968.ca'}
  • id: 6278397
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 42, 'diagramx': [4161, -1, 5978, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 127335166985681277, 711374856192144, 376784618192784, 20922793521841, 124268757511328399, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.E', 'old_label': '84.j1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.J', 'subgroup_fusion': None, 'weyl_group': '139968.ca'}
  • id: 6278398
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 42, 'diagramx': [6985, -1, 6878, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 711374856192144, 2557170678509672397, 376784618192784, 127335254124050613, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.F', 'old_label': '84.k1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.K', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 6278399
    {'ambient': '5878656.d', 'aut_centralizer_order': None, 'aut_label': '84.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2688.A', 'coset_action_label': None, 'count': 42, 'diagramx': [6791, -1, 6816, -1], 'generators': [2554923893160038643, 20354279944770293494, 80784, 43545603, 711374856192144, 2557170678509672397, 2560216252372427973, 376784618192784, 20922793521841, 376610217984000, 5065, 79833840], 'label': '5878656.d.84.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.F', 'old_label': '84.l1', 'projective_image': '5878656.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.L', 'subgroup_fusion': None, 'weyl_group': None}