Abstract group data - 384.18235

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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': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 6, 2, 4, 4, 4, 2, 4, 2], 'aut_gens': [[1, 6, 12, 24, 96], [53, 12, 6, 282, 174], [337, 66, 198, 288, 360], [1, 246, 204, 264, 144], [181, 246, 252, 216, 288], [31, 54, 12, 24, 336], [265, 54, 12, 264, 144], [253, 6, 12, 72, 336], [349, 54, 60, 24, 144], [223, 6, 252, 24, 336]], 'aut_group': '6144.bkh', 'aut_hash': 6836137606128574170, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 132, 'aut_perms': [104212276906507551500933180808753212109901859913371133818163273208173992471592767671801811901122166042978891962410522548561935477018889219176240187035407047690161773296288476654823587571022453004605712912218512393612554734053, 64568666240064903927452742024799925698411654402076026938333421076372081406680136569650649773989067196715016548060587992572212644016002497337448510183186196364426256217475986572441074296197853412763974134003415673817692692996, 22881621573085715407559701949312993391599552812813137586916749374685916781757497470515630800656415782936719903957810311634421084286889314972381240021026435982221901821874008777376805363552940838361794374394399127373785186371, 31265875633239446140714708202582511170988678094977925070799565174049599458405843634255377417090605907279710638846442613023506030698727346951902650476309939781479305771478373745169013525131474866231855633827743012983826044434, 50573355778655215731403838922631061556469650858681232300854652747231947450437461530509649159429488120063256112060394494136119516931333485712043555251582456745899336117130688838842984374571067914108094447472947408611396069799, 12454452171286098809295276823415343115393214509552667631817618929498896792748728442794560921200616668752821038241296689883523616285276252676893116484002150998653291929206021372918119658982144185755618300963120511363262771320, 71172474407381671140564550818065721463248995111294113156358134699459186593394588662098023664098727374250387965809413551790030157084848836237916947089156408360661580449916192999006796082076673532812565626752951938780878256447, 107774516104509054828133277989572763036986762991905906992277853546085307320635364165332092516979768275483708528490133221490979195581958094535928341721316805403872650314069069788872369903965422827311444239627480154404155086383, 50571116588732587658595126761506125583713452677640153080712088067390549202295198749521682219926452360694362711383411974212128570152919373327942754362607173379395889863902619453066085813708933179459141827598618387945431200515], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 4, 1, 1], [2, 6, 2, 1], [2, 12, 1, 3], [3, 64, 2, 1], [4, 12, 1, 2], [4, 12, 2, 2], [6, 64, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.\\GL(2,\\mathbb{Z}/4)', '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': 24, 'autcentquo_group': '6144.bkh', 'autcentquo_hash': 6836137606128574170, 'autcentquo_nilpotent': False, 'autcentquo_order': 6144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^6.\\GL(2,\\mathbb{Z}/4)', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 4, 1], [2, 6, 2], [2, 12, 3], [3, 64, 2], [4, 12, 6], [6, 64, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '384.18235', 'commutator_count': 1, 'commutator_label': '64.242', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 18235, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 4, 1, 1], [2, 6, 1, 2], [2, 12, 1, 3], [3, 64, 2, 1], [4, 12, 1, 6], [6, 64, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 5460, 'exponent': 12, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 2]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '96.229', 'hash': 18235, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 2, 2, 4, 4], 'inner_gens': [[1, 18, 6, 288, 360], [13, 6, 12, 72, 336], [19, 6, 12, 216, 144], [121, 54, 204, 24, 96], [217, 246, 60, 24, 96]], 'inner_hash': 18235, 'inner_nilpotent': False, 'inner_order': 384, 'inner_split': False, 'inner_tex': 'C_2^5:A_4', 'inner_used': [1, 2, 4], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 6], [3, 10], [12, 2]], 'label': '384.18235', 'linC_count': 2, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 2, 'linQ_dim': 12, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^5:A4', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 18, 'number_divisions': 16, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 167, 'number_subgroup_classes': 266, 'number_subgroups': 1718, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 55], [3, 128], [4, 72], [6, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 240, 0, 48], 'outer_gens': [[5, 12, 6, 282, 174], [145, 246, 12, 24, 96], [1, 198, 60, 24, 96], [259, 198, 60, 24, 288]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [288, 7, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [3, 10], [12, 2]], 'representations': {'PC': {'code': 1160374515528963420124477165615196033059449992330214945804608, 'gens': [1, 3, 4, 5, 7], 'pres': [8, 2, 3, 2, 2, 2, 2, 2, 2, 16, 434, 154, 195, 299, 11524, 2412, 500, 748, 116, 9221, 5773, 20166, 6062, 3158, 702, 166, 15367, 1551]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [17999597, 11742068, 10024001, 7533399, 32746561, 5128257, 10726868, 6210625]}, 'Perm': {'d': 16, 'gens': [87107887, 174751733655, 11212821043200, 5606234750016, 2789832694440, 2789705335087, 2789792421136, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5:A_4', 'transitive_degree': 16, '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: 110006303
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 18235, 'group_order': 384, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 110006313
    {'aut_label': '2A', 'centralizer': '3.a1.a1', 'counter': 2, 'group_counter': 18235, 'group_order': 384, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 192, 'size': 3}
  • id: 110006314
    {'aut_label': '2B', 'centralizer': '4.a1.a1', 'counter': 3, 'group_counter': 18235, 'group_order': 384, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 3, 'size': 4}
  • id: 110006315
    {'aut_label': '2C', 'centralizer': '6.e1.a1', 'counter': 4, 'group_counter': 18235, 'group_order': 384, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 15, 'size': 6}
  • id: 110006316
    {'aut_label': '2C', 'centralizer': '6.e1.a1', 'counter': 5, 'group_counter': 18235, 'group_order': 384, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 207, 'size': 6}
  • id: 110006317
    {'aut_label': '2E', 'centralizer': '12.a1.a1', 'counter': 6, 'group_counter': 18235, 'group_order': 384, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 12, 'size': 12}
  • id: 110006318
    {'aut_label': '2F', 'centralizer': '12.q1.a1', 'counter': 7, 'group_counter': 18235, 'group_order': 384, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 30, 'size': 12}
  • id: 110006319
    {'aut_label': '2G', 'centralizer': '12.m1.a1', 'counter': 8, 'group_counter': 18235, 'group_order': 384, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 39, 'size': 12}
  • id: 110006320
    {'aut_label': '3A1', 'centralizer': '64.a1.a1', 'counter': 9, 'group_counter': 18235, 'group_order': 384, 'label': '3A1', 'order': 3, 'powers': [10, 1], 'representative': 70, 'size': 64}
  • id: 110006304
    {'aut_label': '3A1', 'centralizer': '64.a1.a1', 'counter': 10, 'group_counter': 18235, 'group_order': 384, 'label': '3A-1', 'order': 3, 'powers': [9, 1], 'representative': 248, 'size': 64}
  • id: 110006305
    {'aut_label': '4A', 'centralizer': '12.r1.a1', 'counter': 11, 'group_counter': 18235, 'group_order': 384, 'label': '4A', 'order': 4, 'powers': [2, 11], 'representative': 96, 'size': 12}
  • id: 110006306
    {'aut_label': '4A', 'centralizer': '12.r1.b1', 'counter': 12, 'group_counter': 18235, 'group_order': 384, 'label': '4B', 'order': 4, 'powers': [2, 12], 'representative': 108, 'size': 12}
  • id: 110006307
    {'aut_label': '4C', 'centralizer': '12.u1.a1', 'counter': 13, 'group_counter': 18235, 'group_order': 384, 'label': '4C', 'order': 4, 'powers': [2, 13], 'representative': 36, 'size': 12}
  • id: 110006308
    {'aut_label': '4D', 'centralizer': '12.p1.b1', 'counter': 14, 'group_counter': 18235, 'group_order': 384, 'label': '4D', 'order': 4, 'powers': [2, 14], 'representative': 99, 'size': 12}
  • id: 110006309
    {'aut_label': '4D', 'centralizer': '12.p1.a1', 'counter': 15, 'group_counter': 18235, 'group_order': 384, 'label': '4E', 'order': 4, 'powers': [2, 15], 'representative': 111, 'size': 12}
  • id: 110006310
    {'aut_label': '4F', 'centralizer': '12.s1.a1', 'counter': 16, 'group_counter': 18235, 'group_order': 384, 'label': '4F', 'order': 4, 'powers': [2, 16], 'representative': 33, 'size': 12}
  • id: 110006311
    {'aut_label': '6A1', 'centralizer': '64.a1.a1', 'counter': 17, 'group_counter': 18235, 'group_order': 384, 'label': '6A1', 'order': 6, 'powers': [9, 3], 'representative': 251, 'size': 64}
  • id: 110006312
    {'aut_label': '6A1', 'centralizer': '64.a1.a1', 'counter': 18, 'group_counter': 18235, 'group_order': 384, 'label': '6A-1', 'order': 6, 'powers': [10, 3], 'representative': 67, 'size': 64}
• gps_qchar •

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

  
  
  • id: 4476343
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4476351
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4476352
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1], 'schur_index': 1}
  • id: 4476353
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.1d', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, -1, -1, 2, -2, 2, 2, -2, -2, 1, 1], 'schur_index': 1}
  • id: 4476354
    {'cdim': 3, 'counter': 5, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3a', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, -1, -1, -1, 0, 0, -1, -1, 3, -1, 3, -1, 0, 0], 'schur_index': 1}
  • id: 4476355
    {'cdim': 3, 'counter': 6, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3b', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, -1, -1, -1, 0, 0, 3, 3, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4476356
    {'cdim': 3, 'counter': 7, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3c', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, -1, -1, 3, 0, 0, -1, -1, -1, 3, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4476357
    {'cdim': 3, 'counter': 8, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3d', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, -1, 3, -1, 0, 0, -1, -1, -1, -1, -1, 3, 0, 0], 'schur_index': 1}
  • id: 4476358
    {'cdim': 3, 'counter': 9, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3e', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4476344
    {'cdim': 3, 'counter': 10, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3f', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -3, -3, -3, 3, -1, 1, 0, 0, -1, 1, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4476345
    {'cdim': 3, 'counter': 11, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3g', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -3, 1, 1, -1, -1, -3, 0, 0, -1, 1, -1, 3, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4476346
    {'cdim': 3, 'counter': 12, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3h', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -3, 1, 1, -1, -1, 1, 0, 0, -1, 1, 3, -1, -3, 1, 0, 0], 'schur_index': 1}
  • id: 4476347
    {'cdim': 3, 'counter': 13, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3i', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -3, 1, 1, -1, -1, 1, 0, 0, 3, -3, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4476348
    {'cdim': 3, 'counter': 14, 'faithful': False, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.3j', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, 3, -3, 1, 1, -1, 3, 1, 0, 0, -1, 1, -1, -1, 1, -3, 0, 0], 'schur_index': 1}
  • id: 4476349
    {'cdim': 12, 'counter': 15, 'faithful': True, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.12a', 'multiplicity': 1, 'nt': [16, 731], 'qdim': 12, 'qvalues': [12, -4, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4476350
    {'cdim': 12, 'counter': 16, 'faithful': True, 'group': '384.18235', 'group_order': 384, 'image': None, 'label': '384.18235.12b', 'multiplicity': 1, 'nt': [16, 731], 'qdim': 12, 'qvalues': [12, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 6913762
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 384, 'label': '384.18235.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6913772
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 192, 'label': '384.18235.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6913773
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 128, 'label': '384.18235.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 6913774
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 128, 'label': '384.18235.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 6913775
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 64, 'label': '384.18235.1d1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 6913776
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 64, 'label': '384.18235.1d2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 6913777
    {'center': '12.d1.b1', 'center_index': 12, 'center_order': 32, 'counter': 7, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.b1', 'kernel_order': 32, 'label': '384.18235.3a', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913778
    {'center': '12.d1.a1', 'center_index': 12, 'center_order': 32, 'counter': 8, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 32, 'label': '384.18235.3b', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913779
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 32, 'counter': 9, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 32, 'label': '384.18235.3c', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913763
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 32, 'counter': 10, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 32, 'label': '384.18235.3d', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913764
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 32, 'counter': 11, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 32, 'label': '384.18235.3e', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913765
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 32, 'counter': 12, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 16, 'label': '384.18235.3f', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913766
    {'center': '12.c1.a1', 'center_index': 12, 'center_order': 32, 'counter': 13, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.d1.a1', 'kernel_order': 16, 'label': '384.18235.3g', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913767
    {'center': '12.d1.b1', 'center_index': 12, 'center_order': 32, 'counter': 14, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.c1.b1', 'kernel_order': 16, 'label': '384.18235.3h', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913768
    {'center': '12.d1.a1', 'center_index': 12, 'center_order': 32, 'counter': 15, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.c1.a1', 'kernel_order': 16, 'label': '384.18235.3i', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913769
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 32, 'counter': 16, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.a1', 'kernel_order': 16, 'label': '384.18235.3j', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913770
    {'center': '384.a1.a1', 'center_index': 384, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '384.18235', 'image_order': 384, 'indicator': 1, 'kernel': '384.a1.a1', 'kernel_order': 1, 'label': '384.18235.12a', 'nt': [16, 731], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6913771
    {'center': '384.a1.a1', 'center_index': 384, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '384.18235', 'group_counter': 18235, 'group_order': 384, 'image': None, 'image_isoclass': '384.18235', 'image_order': 384, 'indicator': 1, 'kernel': '384.a1.a1', 'kernel_order': 1, 'label': '384.18235.12b', 'nt': [16, 731], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 66020834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 384, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '384.18235.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18235', 'subgroup_hash': 18235, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 192, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1023', 'subgroup_hash': 1023, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66021023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 2, 'label': '384.18235.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2264', 'subgroup_hash': 2264, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 2}
  • id: 66021034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.4.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66021045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.4.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66021056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.4.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.72', 'subgroup_hash': 72, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 66021067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.4.d1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.71', 'subgroup_hash': 71, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 66021078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 32, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.4.d1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.71', 'subgroup_hash': 71, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 66021089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.219', 'subgroup_hash': 219, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.219', 'subgroup_hash': 219, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.232', 'subgroup_hash': 232, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.241', 'subgroup_hash': 241, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 66020979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 66020990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 66021001
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 66021012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 66021050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 66021051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.12.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66021080
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66021081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.16.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66021082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66021083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.16.b1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.b2', 'outer_equivalence': False, 'perfect': False, '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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66021084
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 66021085
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 66021086
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021088
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021092
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 66021093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 66021094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66021099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020838
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 66020839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 66020844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020849
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 66020858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020876
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020882
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 66020889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020893
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.32.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.32.b1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.a3', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.32.b1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.a4', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.32.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66020900
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 159, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020902
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020904
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.b2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020905
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.b2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020909
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020910
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.e2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.e2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020921
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020922
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020926
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020927
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020929
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.j1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.b2', 'outer_equivalence': False, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.j2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 66020949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020953
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020954
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bd1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020962
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bd1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.b2', 'outer_equivalence': False, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020964
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bd2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bd2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bd2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.48.bd2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd2.b2', 'outer_equivalence': False, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 66020969
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66020970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18235.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.229', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 229, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:A_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'S', 'D2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020973
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020974
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.c2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.c2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020976
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020977
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.d2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020978
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.d2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020980
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.e2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020982
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.e2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020983
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020984
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.f2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020985
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.f2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020987
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.96.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020991
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.96.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020992
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 241, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66020993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020994
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.k1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020995
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020996
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.k1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020997
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020998
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66020999
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021000
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021002
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.m2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021003
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.m2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021004
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021005
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.n1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021006
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.n1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.a3', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021007
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.n1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.a4', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021008
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021009
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.18235.96.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66021010
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '384.18235.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 66021011
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021013
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021014
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.192.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021015
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.192.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021016
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.192.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021017
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.192.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021018
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '384.18235.192.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66021019
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '384.18235', 'ambient_counter': 18235, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': True, 'central_factor': False, 'centralizer_order': 384, 'characteristic': True, 'core_order': 1, 'counter': 266, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '384.18235.384.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '384.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '384.18235', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18235, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5:A_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D3', 'C5'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 66020834
    {'ambient': '384.18235', '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': '384.a1.a1', 'complements': ['384.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.d1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4254, 4380, 7166, 4406, 992, 3303, 8806, 3075], 'generators': [3, 24, 96, 2, 12, 192, 48, 6], 'label': '384.18235.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '384.18235'}
  • id: 66020835
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56092', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.b1', '12.f1.b1', '12.g1.b1', '12.h1.a1', '12.i1.b1', '12.j1.a1', '12.k1.a1', '12.l1.b1', '12.p1.b1', '12.r1.b1', '12.t1.b1', '12.ba1.b1', '12.bd1.a1', '12.bg1.b1', '12.bi1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6210, -1, 3462, -1, 6201, -1, 3677, -1], 'generators': [3, 18, 348, 216], 'label': '384.18235.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66020836
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1'], 'contains': ['48.e2.a1', '48.f1.b1', '48.g1.a1', '48.h1.a1', '48.j1.b1', '48.k1.a1', '48.m1.b1'], 'core': '384.a1.a1', 'coset_action_label': '24T1024', 'count': 12, 'diagramx': [2349, -1, 7662, -1, 2899, -1, 7298, -1], 'generators': [15, 18, 336], 'label': '384.18235.24.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '24.i1.c1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020837
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.b1'], 'contains': ['48.e2.a2', '48.f1.a1', '48.g1.b1', '48.h1.b1', '48.j1.b2', '48.k1.b1', '48.m1.a1'], 'core': '384.a1.a1', 'coset_action_label': '24T1024', 'count': 12, 'diagramx': [2349, -1, 7460, -1, 2899, -1, 7833, -1], 'generators': [171, 18, 180], 'label': '384.18235.24.i1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.b1', 'old_label': '24.i1.d1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020838
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.e1.a1', '12.f1.a1', '12.f1.b1', '12.g1.a1', '12.g1.b1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '48.b2.a1', '48.b2.a2', '48.v1.a1', '48.w1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1126, -1, 8474, -1, 1922, -1, 8766, -1], 'generators': [3, 18, 48, 192], 'label': '384.18235.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.j1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020839
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.a1', '12.f1.a1', '12.f1.b1', '12.i1.a1', '12.i1.b1', '12.j1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '48.x1.a1', '48.bc1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2604, -1, 6352, -1, 2677, -1, 7149, -1], 'generators': [3, 180, 48], 'label': '384.18235.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.k1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020840
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.e1.a1', '12.g1.a1', '12.g1.b1', '12.i1.a1', '12.i1.b1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.y1.a1', '48.ba1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4805, -1, 3536, -1, 6512, -1, 5669, -1], 'generators': [3, 186, 48], 'label': '384.18235.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.l1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020841
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.z1.a1', '48.bb1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4660, -1, 5524, -1, 5111, -1, 4534, -1], 'generators': [3, 168], 'label': '384.18235.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.m1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020842
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.f1.b1', '12.g1.b1', '12.h1.a1', '12.i1.b1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.z1.b1', '48.bb1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4660, -1, 4637, -1, 5111, -1, 4657, -1], 'generators': [3, 174], 'label': '384.18235.24.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.m1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020843
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.m1.a1', '12.n1.a1', '12.n1.b1', '12.q1.a1', '12.v1.a1', '12.v1.b1'], 'contains': ['48.e1.a1', '48.e1.b1', '48.e2.a1', '48.e2.a2', '48.v1.a1', '48.x1.a1', '48.y1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2477, -1, 6913, -1, 3078, -1, 7565, -1], 'generators': [9, 180, 48, 192], 'label': '384.18235.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.n1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020844
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.l1.a1', '12.o1.b1', '12.p1.a1', '12.q1.a1', '12.v1.b1', '12.w1.a1'], 'contains': ['48.f1.a1', '48.f1.c1', '48.v1.a1', '48.x1.a1', '48.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2922, -1, 6844, -1, 3700, -1, 6852, -1], 'generators': [171, 180, 192], 'label': '384.18235.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020845
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '12.l1.b1', '12.o1.a1', '12.p1.b1', '12.q1.a1', '12.v1.a1', '12.w1.a1'], 'contains': ['48.f1.b1', '48.f1.d1', '48.v1.a1', '48.x1.a1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2922, -1, 6611, -1, 3700, -1, 6704, -1], 'generators': [177, 180, 192], 'label': '384.18235.24.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020846
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56092', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1', '12.l1.a1', '12.p1.a1', '12.r1.a1', '12.t1.a1', '12.ba1.a1', '12.bd1.b1', '12.bg1.a1', '12.bi1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6210, -1, 4650, -1, 6201, -1, 3282, -1], 'generators': [3, 18, 168, 336], 'label': '384.18235.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66020847
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.l1.a1', '12.n1.a1', '12.r1.a1', '12.s1.a1', '12.v1.a1', '12.x1.a1'], 'contains': ['48.g1.a1', '48.g1.c1', '48.v1.a1', '48.y1.a1', '48.z1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5077, -1, 5256, -1, 6734, -1, 1313, -1], 'generators': [21, 168, 192], 'label': '384.18235.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020848
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '12.l1.b1', '12.n1.b1', '12.r1.b1', '12.s1.a1', '12.v1.b1', '12.x1.a1'], 'contains': ['48.g1.b1', '48.g1.d1', '48.v1.a1', '48.y1.a1', '48.z1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5077, -1, 1760, -1, 6734, -1, 2142, -1], 'generators': [15, 174, 192], 'label': '384.18235.24.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020849
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.l1.b1', '12.p1.a1', '12.r1.a1', '12.t1.b1', '12.v1.a1', '12.y1.a1'], 'contains': ['48.h1.a1', '48.v1.a1', '48.z1.a1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5460, -1, 5747, -1, 6091, -1, 3490, -1], 'generators': [9, 168, 192], 'label': '384.18235.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.q1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020850
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.q1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.l1.a1', '12.p1.b1', '12.r1.b1', '12.t1.a1', '12.v1.b1', '12.y1.b1'], 'contains': ['48.h1.b1', '48.v1.a1', '48.z1.b1', '48.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5460, -1, 4552, -1, 6091, -1, 4027, -1], 'generators': [171, 174, 192], 'label': '384.18235.24.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.q1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020851
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.m1.a1', '12.o1.a1', '12.r1.a1', '12.t1.a1', '12.x1.a1', '12.y1.a1'], 'contains': ['48.v1.a1', '48.z1.a1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6819, -1, 4019, -1, 6310, -1, 1571, -1], 'generators': [15, 168], 'label': '384.18235.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.r1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020852
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '12.m1.a1', '12.o1.b1', '12.r1.b1', '12.t1.b1', '12.x1.a1', '12.y1.b1'], 'contains': ['48.v1.a1', '48.z1.b1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6819, -1, 2203, -1, 6310, -1, 2277, -1], 'generators': [183, 174], 'label': '384.18235.24.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.r1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020853
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.n1.b1', '12.p1.a1', '12.t1.a1', '12.u1.a1', '12.w1.a1', '12.y1.b1'], 'contains': ['48.v1.a1', '48.ba1.a1', '48.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6079, -1, 3457, -1, 8040, -1, 5024, -1], 'generators': [171, 186], 'label': '384.18235.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.s1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020854
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '12.n1.a1', '12.p1.b1', '12.t1.b1', '12.u1.a1', '12.w1.a1', '12.y1.a1'], 'contains': ['48.v1.a1', '48.ba1.a1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6079, -1, 5016, -1, 8040, -1, 4779, -1], 'generators': [15, 186], 'label': '384.18235.24.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.s1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020855
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '24.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.o1.a1', '12.o1.b1', '12.s1.a1', '12.u1.a1', '12.y1.a1', '12.y1.b1'], 'contains': ['48.i1.a1', '48.i1.b1', '48.v1.a1', '48.ba1.a1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8773, -1, 2763, -1, 8543, -1, 3097, -1], 'generators': [183, 186, 48], 'label': '384.18235.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.t1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020856
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.v1.a1', '12.v1.b1', '12.w1.a1', '12.x1.a1', '12.y1.a1', '12.y1.b1'], 'contains': ['48.j1.a1', '48.j1.a2', '48.j1.b1', '48.j1.b2', '48.j2.a1', '48.v1.a1', '48.w1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1030, -1, 8423, -1, 2055, -1, 8678, -1], 'generators': [15, 18, 48, 192], 'label': '384.18235.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.u1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020857
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6249567', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.c1.a1', '12.e1.a1', '12.g1.a1', '12.g1.b1', '12.i1.a1', '12.i1.b1', '12.k1.a1', '12.n1.a1', '12.n1.b1', '12.s1.a1', '12.u1.a1', '12.bb1.a1', '12.bc1.a1', '12.bh1.a1', '12.bh1.b1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7133, -1, 2957, -1, 8400, -1, 4127, -1], 'generators': [3, 18, 348, 168], 'label': '384.18235.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66020858
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.v1.a1', '12.z1.a1', '12.ba1.a1', '12.bd1.b1', '12.bf1.a1', '12.bj1.a1'], 'contains': ['48.k1.a1', '48.w1.a1', '48.x1.a1', '48.z1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3082, -1, 6758, -1, 3256, -1, 6407, -1], 'generators': [18, 336, 48], 'label': '384.18235.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.v1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020859
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '12.v1.b1', '12.z1.b1', '12.ba1.b1', '12.bd1.a1', '12.bf1.a1', '12.bj1.a1'], 'contains': ['48.k1.b1', '48.w1.a1', '48.x1.a1', '48.z1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3082, -1, 6525, -1, 3256, -1, 6555, -1], 'generators': [18, 180, 192], 'label': '384.18235.24.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.v1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020860
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.w1.a1', '12.bb1.a1', '12.bc1.a1', '12.be1.a1', '12.bf1.a1', '12.bj1.a1'], 'contains': ['48.l1.a1', '48.w1.a1', '48.x1.a1', '48.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2764, -1, 6439, -1, 3478, -1, 7001, -1], 'generators': [18, 228, 192], 'label': '384.18235.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.w1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020861
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.v1.b1', '12.ba1.a1', '12.bb1.a1', '12.bg1.a1', '12.bh1.b1', '12.bk1.a1'], 'contains': ['48.m1.a1', '48.w1.a1', '48.y1.a1', '48.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3845, -1, 5654, -1, 5535, -1, 5966, -1], 'generators': [171, 18, 192], 'label': '384.18235.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.x1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020862
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '12.v1.a1', '12.ba1.b1', '12.bb1.a1', '12.bg1.b1', '12.bh1.a1', '12.bk1.a1'], 'contains': ['48.m1.b1', '48.w1.a1', '48.y1.a1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3845, -1, 5910, -1, 5535, -1, 5817, -1], 'generators': [351, 18, 48], 'label': '384.18235.24.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.x1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020863
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.x1.a1', '12.z1.a1', '12.z1.b1', '12.bh1.a1', '12.bh1.b1', '12.bk1.a1'], 'contains': ['48.n1.a1', '48.w1.a1', '48.y1.a1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3504, -1, 3327, -1, 4105, -1, 4309, -1], 'generators': [231, 18, 192], 'label': '384.18235.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.y1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020864
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.y1.a1', '12.bc1.a1', '12.bd1.b1', '12.bh1.a1', '12.bi1.a1', '12.bj1.a1'], 'contains': ['48.w1.a1', '48.z1.a1', '48.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6951, -1, 4732, -1, 7857, -1, 3636, -1], 'generators': [18, 168], 'label': '384.18235.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.z1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020865
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '12.y1.b1', '12.bc1.a1', '12.bd1.a1', '12.bh1.b1', '12.bi1.b1', '12.bj1.a1'], 'contains': ['48.w1.a1', '48.z1.b1', '48.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6951, -1, 2514, -1, 7857, -1, 3759, -1], 'generators': [18, 348], 'label': '384.18235.24.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.z1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020866
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.x1.a1', '12.bd1.a1', '12.bd1.b1', '12.bg1.a1', '12.bg1.b1', '12.bj1.a1'], 'contains': ['48.w1.a1', '48.z1.a1', '48.z1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3358, -1, 3889, -1, 4307, -1, 1693, -1], 'generators': [18, 216], 'label': '384.18235.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.ba1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020867
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.y1.b1', '12.z1.b1', '12.be1.a1', '12.bg1.a1', '12.bi1.a1', '12.bk1.a1'], 'contains': ['48.w1.a1', '48.bb1.a1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5716, -1, 3614, -1, 5738, -1, 5147, -1], 'generators': [339, 18], 'label': '384.18235.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bb1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020868
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6249567', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.f1.a1', '12.f1.b1', '12.i1.a1', '12.i1.b1', '12.j1.a1', '12.m1.a1', '12.o1.a1', '12.o1.b1', '12.q1.a1', '12.z1.a1', '12.z1.b1', '12.be1.a1', '12.bf1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4163, -1, 5448, -1, 4578, -1, 5086, -1], 'generators': [3, 18, 180, 336], 'label': '384.18235.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66020869
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '12.y1.a1', '12.z1.a1', '12.be1.a1', '12.bg1.b1', '12.bi1.b1', '12.bk1.a1'], 'contains': ['48.w1.a1', '48.bb1.b1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5716, -1, 4946, -1, 5738, -1, 4902, -1], 'generators': [183, 18], 'label': '384.18235.24.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bb1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020870
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.w1.a1', '12.ba1.a1', '12.ba1.b1', '12.bi1.a1', '12.bi1.b1', '12.bk1.a1'], 'contains': ['48.w1.a1', '48.bb1.a1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3227, -1, 5831, -1, 3902, -1, 6101, -1], 'generators': [219, 18], 'label': '384.18235.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bc1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020871
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.l1.a1', '12.n1.b1', '12.q1.a1', '12.z1.b1', '12.ba1.a1', '12.bb1.a1'], 'contains': ['48.p1.a1', '48.x1.a1', '48.y1.a1', '48.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4345, -1, 5170, -1, 5314, -1, 5521, -1], 'generators': [339, 180, 192], 'label': '384.18235.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020872
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.l1.b1', '12.n1.a1', '12.q1.a1', '12.z1.a1', '12.ba1.b1', '12.bb1.a1'], 'contains': ['48.p1.b1', '48.x1.a1', '48.y1.a1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4345, -1, 5995, -1, 5314, -1, 5372, -1], 'generators': [345, 180, 192], 'label': '384.18235.24.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020873
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.bb1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.n1.a1', '12.o1.a1', '12.p1.a1', '12.bc1.a1', '12.bd1.b1', '12.bf1.a1'], 'contains': ['48.x1.a1', '48.z1.a1', '48.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6484, -1, 4850, -1, 7674, -1, 3344, -1], 'generators': [354, 216], 'label': '384.18235.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.be1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020874
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.n1.b1', '12.o1.b1', '12.p1.b1', '12.bc1.a1', '12.bd1.a1', '12.bf1.a1'], 'contains': ['48.x1.a1', '48.z1.b1', '48.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6484, -1, 2916, -1, 7674, -1, 3881, -1], 'generators': [186, 348], 'label': '384.18235.24.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.be1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020875
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.l1.a1', '12.l1.b1', '12.m1.a1', '12.bd1.a1', '12.bd1.b1', '12.bf1.a1'], 'contains': ['48.x1.a1', '48.z1.a1', '48.z1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4529, -1, 4467, -1, 4928, -1, 1448, -1], 'generators': [354, 168], 'label': '384.18235.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bf1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020876
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '24.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.p1.a1', '12.p1.b1', '12.q1.a1', '12.ba1.a1', '12.ba1.b1', '12.be1.a1'], 'contains': ['48.q1.a1', '48.x1.a1', '48.bb1.a1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3674, -1, 6088, -1, 4526, -1, 6248, -1], 'generators': [219, 180, 48], 'label': '384.18235.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bg1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020877
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.m1.a1', '12.o1.a1', '12.o1.b1', '12.z1.a1', '12.z1.b1', '12.be1.a1'], 'contains': ['48.x1.a1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5304, -1, 4089, -1, 4745, -1, 4174, -1], 'generators': [225, 180], 'label': '384.18235.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bh1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020878
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.l1.b1', '12.n1.a1', '12.r1.a1', '12.ba1.a1', '12.bg1.b1', '12.bh1.a1'], 'contains': ['48.y1.a1', '48.z1.a1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6222, -1, 3819, -1, 7237, -1, 1906, -1], 'generators': [351, 168], 'label': '384.18235.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bi1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020879
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '12.f1.a1', '12.f1.b1', '12.g1.a1', '12.g1.b1', '12.h1.a1', '12.v1.a1', '12.v1.b1', '12.w1.a1', '12.x1.a1', '12.y1.a1', '12.y1.b1', '12.bj1.a1', '12.bk1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3258, -1, 6272, -1, 3468, -1, 6948, -1], 'generators': [3, 18, 12, 168], 'label': '384.18235.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020880
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.z1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.l1.a1', '12.n1.b1', '12.r1.b1', '12.ba1.b1', '12.bg1.a1', '12.bh1.b1'], 'contains': ['48.y1.a1', '48.z1.b1', '48.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6222, -1, 1838, -1, 7237, -1, 2600, -1], 'generators': [219, 174], 'label': '384.18235.24.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bi1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020881
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.m1.a1', '12.r1.a1', '12.s1.a1', '12.z1.a1', '12.bg1.a1', '12.bh1.a1'], 'contains': ['48.s1.a1', '48.y1.a1', '48.z1.a1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7215, -1, 2119, -1, 7455, -1, 983, -1], 'generators': [345, 168, 192], 'label': '384.18235.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bj1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020882
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '24.bj1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.m1.a1', '12.r1.b1', '12.s1.a1', '12.z1.b1', '12.bg1.b1', '12.bh1.b1'], 'contains': ['48.s1.b1', '48.y1.a1', '48.z1.b1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7215, -1, 1581, -1, 7455, -1, 1154, -1], 'generators': [231, 174, 192], 'label': '384.18235.24.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bj1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020883
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.n1.a1', '12.n1.b1', '12.s1.a1', '12.bb1.a1', '12.bh1.a1', '12.bh1.b1'], 'contains': ['48.t1.a1', '48.y1.a1', '48.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7787, -1, 1673, -1, 8781, -1, 2836, -1], 'generators': [231, 186, 48], 'label': '384.18235.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bk1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020884
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.o1.a1', '12.r1.a1', '12.t1.b1', '12.z1.a1', '12.bg1.b1', '12.bi1.a1'], 'contains': ['48.z1.a1', '48.bb1.b1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7070, -1, 3679, -1, 7070, -1, 2017, -1], 'generators': [357, 168], 'label': '384.18235.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bl1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020885
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.z1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.o1.b1', '12.r1.b1', '12.t1.a1', '12.z1.b1', '12.bg1.a1', '12.bi1.b1'], 'contains': ['48.z1.b1', '48.bb1.a1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7070, -1, 1903, -1, 7070, -1, 2389, -1], 'generators': [339, 174], 'label': '384.18235.24.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bl1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020886
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.bb1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.l1.a1', '12.p1.a1', '12.t1.a1', '12.ba1.a1', '12.bg1.a1', '12.bi1.a1'], 'contains': ['48.z1.a1', '48.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6700, -1, 3955, -1, 6921, -1, 2489, -1], 'generators': [339, 168], 'label': '384.18235.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bm1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020887
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.l1.b1', '12.p1.b1', '12.t1.b1', '12.ba1.b1', '12.bg1.b1', '12.bi1.b1'], 'contains': ['48.z1.b1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6700, -1, 2448, -1, 6921, -1, 2712, -1], 'generators': [351, 174], 'label': '384.18235.24.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bm1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020888
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '48.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.s1.a1', '12.t1.a1', '12.t1.b1', '12.bc1.a1', '12.bd1.a1', '12.bd1.b1'], 'contains': ['48.u1.a1', '48.z1.a1', '48.z1.b1', '48.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8944, -1, 1975, -1, 9003, -1, 824, -1], 'generators': [186, 336, 48], 'label': '384.18235.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bn1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020889
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.o1.b1', '12.t1.a1', '12.u1.a1', '12.be1.a1', '12.bh1.b1', '12.bi1.a1'], 'contains': ['48.ba1.a1', '48.bb1.a1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8628, -1, 2851, -1, 8207, -1, 3232, -1], 'generators': [219, 186], 'label': '384.18235.24.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bo1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020890
    {'ambient': '384.18235', 'aut_centralizer_order': 8, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.l1.a1', '12.m1.a1', '12.n1.b1', '12.o1.b1', '12.r1.b1', '12.s1.a1', '12.t1.a1', '12.v1.b1', '12.x1.a1', '12.y1.b1', '12.z1.b1', '12.bd1.a1', '12.bg1.a1', '12.bh1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6458, -1, 2215, -1, 6943, -1, 2090, -1], 'generators': [339, 18, 348, 216], 'label': '384.18235.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66020891
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '48.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.o1.a1', '12.t1.b1', '12.u1.a1', '12.be1.a1', '12.bh1.a1', '12.bi1.b1'], 'contains': ['48.ba1.a1', '48.bb1.b1', '48.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8628, -1, 2330, -1, 8207, -1, 2961, -1], 'generators': [351, 186], 'label': '384.18235.24.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bo1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66020892
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '24.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.p1.a1', '12.p1.b1', '12.u1.a1', '12.bb1.a1', '12.bi1.a1', '12.bi1.b1'], 'contains': ['48.ba1.a1', '48.bb1.a1', '48.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8527, -1, 3396, -1, 8348, -1, 4428, -1], 'generators': [339, 186], 'label': '384.18235.24.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bp1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66020893
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.c1.b1', '8.d1.a1', '16.a1.a1'], 'contains': ['96.a1.a1', '128.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1532, -1, 8129, -1, 814, -1, 8938, -1], 'generators': [2, 48, 192], 'label': '384.18235.32.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66020894
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a1'], 'contains': ['96.n1.a1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '32T9338', 'count': 16, 'diagramx': [149, -1, 9954, -1, 343, -1, 9498, -1], 'generators': [2, 18, 12], 'label': '384.18235.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '32.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66020895
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a2'], 'contains': ['96.n1.a2', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '32T9338', 'count': 16, 'diagramx': [149, -1, 9831, -1, 343, -1, 9739, -1], 'generators': [2, 258, 60], 'label': '384.18235.32.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '32.b1.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66020896
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.b1'], 'contains': ['96.n1.a3', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '32T9338', 'count': 16, 'diagramx': [149, -1, 9622, -1, 343, -1, 9661, -1], 'generators': [2, 66, 204], 'label': '384.18235.32.b1.a3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '32.b1.a3', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a3', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66020897
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.b2'], 'contains': ['96.n1.a4', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '32T9338', 'count': 16, 'diagramx': [149, -1, 9762, -1, 343, -1, 9936, -1], 'generators': [2, 210, 252], 'label': '384.18235.32.b1.a4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '32.b1.a4', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a4', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66020898
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['96.o1.a1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '32T9324', 'count': 32, 'diagramx': [515, -1, 9220, -1, 698, -1, 9094, -1], 'generators': [2, 306, 324], 'label': '384.18235.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.c1.a1', 'old_label': '32.c1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66020899
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['96.o1.a2', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '32T9324', 'count': 32, 'diagramx': [515, -1, 9175, -1, 698, -1, 9016, -1], 'generators': [2, 114, 180], 'label': '384.18235.32.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.c1.a2', 'old_label': '32.c1.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66020900
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.a1', 'aut_quo_index': 60, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.m1.b1'], 'contains': ['96.a1.a1', '96.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2560, 6562, 6001, 6709, 3034, 6936, 6601, 6813], 'generators': [3, 48, 192], 'label': '384.18235.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': -64, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.c1.a1', '12.b1.a1', '12.d1.a1', '12.d1.b1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': '12.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66020901
    {'ambient': '384.18235', 'aut_centralizer_order': 8, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.l1.b1', '12.m1.a1', '12.n1.a1', '12.o1.a1', '12.r1.a1', '12.s1.a1', '12.t1.b1', '12.v1.a1', '12.x1.a1', '12.y1.a1', '12.z1.a1', '12.bd1.b1', '12.bg1.b1', '12.bh1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6458, -1, 4189, -1, 6943, -1, 1874, -1], 'generators': [15, 18, 168, 336], 'label': '384.18235.6.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66020902
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.f1.b1', '24.j1.a1'], 'contains': ['96.b1.a1', '96.c1.a1', '96.d1.a1', '96.k1.a1', '96.k1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1543, -1, 7929, -1, 2208, -1, 8541, -1], 'generators': [3, 18, 240], 'label': '384.18235.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020903
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.f1.a1', '24.j1.a1'], 'contains': ['96.b1.a1', '96.c1.b1', '96.d1.a1', '96.k1.b1', '96.k1.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1543, -1, 8081, -1, 2208, -1, 8718, -1], 'generators': [195, 18, 240], 'label': '384.18235.48.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.b1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020904
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.b2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.f1.b1', '24.j1.a1'], 'contains': ['96.b1.a1', '96.c2.a1', '96.d2.a1', '96.k1.a1', '96.k1.a2', '96.k1.b1', '96.k1.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1656, -1, 8545, -1, 2075, -1, 8896, -1], 'generators': [3, 18, 192], 'label': '384.18235.48.b2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.b2.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020905
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.b2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.f1.b1', '24.j1.a1'], 'contains': ['96.b1.a1', '96.c2.a2', '96.d2.a2', '96.k1.a1', '96.k1.a2', '96.k1.b1', '96.k1.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1656, -1, 8670, -1, 2075, -1, 8807, -1], 'generators': [3, 18, 48], 'label': '384.18235.48.b2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.b2.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b2.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020906
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.e1.b1', '24.k1.a1'], 'contains': ['96.b1.a1', '96.e1.a1', '96.j1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2649, -1, 5782, -1, 2660, -1, 7842, -1], 'generators': [3, 180], 'label': '384.18235.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '48.c1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020907
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.e1.b1', '24.l1.a1'], 'contains': ['96.b1.a1', '96.f1.a1', '96.h1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3421, -1, 5386, -1, 4244, -1, 7389, -1], 'generators': [3, 186], 'label': '384.18235.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '48.d1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020908
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.g1.a1', '24.n1.a1'], 'contains': ['96.c1.a1', '96.e1.a1', '96.f1.a1', '96.l1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2249, -1, 6331, -1, 2901, -1, 7669, -1], 'generators': [9, 180, 192], 'label': '384.18235.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.e1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020909
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.g1.b1', '24.n1.a1'], 'contains': ['96.c1.b1', '96.e1.a1', '96.f1.a1', '96.l1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2249, -1, 6279, -1, 2901, -1, 7925, -1], 'generators': [57, 180, 192], 'label': '384.18235.48.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.e1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020910
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.e2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.i1.c1', '24.n1.a1'], 'contains': ['96.c2.a2', '96.e2.a1', '96.f2.a1', '96.l1.a1', '96.l1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2465, -1, 7257, -1, 3167, -1, 7002, -1], 'generators': [9, 180, 240], 'label': '384.18235.48.e2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '48.e2.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020911
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.e2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.i1.d1', '24.n1.a1'], 'contains': ['96.c2.a1', '96.e2.a2', '96.f2.a2', '96.l1.a1', '96.l1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2465, -1, 7148, -1, 3167, -1, 7758, -1], 'generators': [9, 180, 48], 'label': '384.18235.48.e2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.b1', 'old_label': '48.e2.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e2.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020912
    {'ambient': '384.18235', 'aut_centralizer_order': 8, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.o1.a1', '12.o1.b1', '12.p1.a1', '12.p1.b1', '12.t1.a1', '12.t1.b1', '12.u1.a1', '12.w1.a1', '12.y1.a1', '12.y1.b1', '12.bc1.a1', '12.be1.a1', '12.bi1.a1', '12.bi1.b1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7904, -1, 3705, -1, 7930, -1, 3867, -1], 'generators': [339, 18, 348, 168], 'label': '384.18235.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66020913
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.i1.d1', '24.o1.a1'], 'contains': ['96.c1.a1', '96.e2.a2', '96.i1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2825, -1, 6852, -1, 3291, -1, 6918, -1], 'generators': [171, 180], 'label': '384.18235.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.f1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020914
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.i1.c1', '24.o1.b1'], 'contains': ['96.c1.a1', '96.e2.a1', '96.i1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2825, -1, 6510, -1, 3291, -1, 6292, -1], 'generators': [177, 180], 'label': '384.18235.48.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.f1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020915
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '24.i1.b1', '24.o1.a1'], 'contains': ['96.c1.b1', '96.e2.a2', '96.i1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2825, -1, 6794, -1, 3291, -1, 7467, -1], 'generators': [363, 180], 'label': '384.18235.48.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.f1.c1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020916
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '24.i1.a1', '24.o1.b1'], 'contains': ['96.c1.b1', '96.e2.a1', '96.i1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2825, -1, 6685, -1, 3291, -1, 6684, -1], 'generators': [369, 180], 'label': '384.18235.48.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.f1.d1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020917
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.i1.c1', '24.p1.a1'], 'contains': ['96.c1.a1', '96.f2.a1', '96.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4977, -1, 5052, -1, 5900, -1, 2512, -1], 'generators': [21, 168], 'label': '384.18235.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.b1', 'old_label': '48.g1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020918
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.i1.d1', '24.p1.b1'], 'contains': ['96.c1.a1', '96.f2.a2', '96.g1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4977, -1, 2882, -1, 5900, -1, 2894, -1], 'generators': [15, 174], 'label': '384.18235.48.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.g1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020919
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '24.i1.a1', '24.p1.a1'], 'contains': ['96.c1.b1', '96.f2.a1', '96.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4977, -1, 5152, -1, 5900, -1, 2668, -1], 'generators': [213, 168], 'label': '384.18235.48.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.b1', 'old_label': '48.g1.c1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020920
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '24.i1.b1', '24.p1.b1'], 'contains': ['96.c1.b1', '96.f2.a2', '96.g1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4977, -1, 2792, -1, 5900, -1, 2972, -1], 'generators': [207, 174], 'label': '384.18235.48.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.g1.d1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020921
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.i1.c1', '24.q1.a1'], 'contains': ['96.c2.a2', '96.g1.a1', '96.i1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4060, -1, 6619, -1, 4529, -1, 5934, -1], 'generators': [9, 168], 'label': '384.18235.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '48.h1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020922
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.q1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.i1.d1', '24.q1.b1'], 'contains': ['96.c2.a1', '96.g1.b1', '96.i1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4060, -1, 6444, -1, 4529, -1, 6405, -1], 'generators': [171, 174], 'label': '384.18235.48.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.b1', 'old_label': '48.h1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020923
    {'ambient': '384.18235', 'aut_centralizer_order': 8, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.l1.a1', '12.l1.b1', '12.n1.a1', '12.n1.b1', '12.p1.a1', '12.p1.b1', '12.q1.a1', '12.v1.a1', '12.v1.b1', '12.w1.a1', '12.ba1.a1', '12.ba1.b1', '12.bb1.a1', '12.bf1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3990, -1, 5933, -1, 5289, -1, 6275, -1], 'generators': [219, 18, 180, 336], 'label': '384.18235.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66020924
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.h1.a1', '24.t1.a1'], 'contains': ['96.c1.a1', '96.h1.a1', '96.j1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6800, -1, 3150, -1, 7895, -1, 3859, -1], 'generators': [183, 186], 'label': '384.18235.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.i1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020925
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.h1.b1', '24.t1.a1'], 'contains': ['96.c1.b1', '96.h1.a1', '96.j1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6800, -1, 3240, -1, 7895, -1, 4007, -1], 'generators': [135, 186], 'label': '384.18235.48.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.i1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020926
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.i1.a1', '24.u1.a1'], 'contains': ['96.c1.b1', '96.c2.a2', '96.d2.a1', '96.m1.b1', '96.m2.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1820, -1, 7877, -1, 2340, -1, 8274, -1], 'generators': [63, 18, 192], 'label': '384.18235.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.j1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020927
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.i1.b1', '24.u1.a1'], 'contains': ['96.c1.b1', '96.c2.a1', '96.d2.a2', '96.m1.b1', '96.m2.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1820, -1, 7615, -1, 2340, -1, 8452, -1], 'generators': [207, 18, 48], 'label': '384.18235.48.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.j1.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020928
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.i1.c1', '24.u1.a1'], 'contains': ['96.c1.a1', '96.c2.a2', '96.d2.a1', '96.m1.a1', '96.m2.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1820, -1, 7825, -1, 2340, -1, 8185, -1], 'generators': [15, 18, 192], 'label': '384.18235.48.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.j1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020929
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.i1.d1', '24.u1.a1'], 'contains': ['96.c1.a1', '96.c2.a1', '96.d2.a2', '96.m1.a1', '96.m2.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1820, -1, 7666, -1, 2340, -1, 8363, -1], 'generators': [15, 18, 48], 'label': '384.18235.48.j1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.j1.b2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020930
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.j2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.f1.b1', '24.u1.a1'], 'contains': ['96.c2.a1', '96.c2.a2', '96.d1.a1', '96.m1.a1', '96.m1.b1', '96.m2.a1', '96.m2.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1338, -1, 8211, -1, 1942, -1, 8629, -1], 'generators': [15, 18, 240], 'label': '384.18235.48.j2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.j2.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020931
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.i1.c1', '24.v1.a1'], 'contains': ['96.d2.a1', '96.e2.a1', '96.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2958, -1, 6943, -1, 3525, -1, 6214, -1], 'generators': [18, 336], 'label': '384.18235.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '48.k1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020932
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.i1.d1', '24.v1.b1'], 'contains': ['96.d2.a2', '96.e2.a2', '96.g1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2958, -1, 6897, -1, 3525, -1, 7311, -1], 'generators': [18, 180], 'label': '384.18235.48.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.b1', 'old_label': '48.k1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020933
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.e1.b1', '24.w1.a1'], 'contains': ['96.d1.a1', '96.e1.a1', '96.h1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2733, -1, 5840, -1, 2776, -1, 7545, -1], 'generators': [18, 228], 'label': '384.18235.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '48.l1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020934
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.6249567', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.z1.a1', '12.z1.b1', '12.ba1.a1', '12.ba1.b1', '12.bb1.a1', '12.be1.a1', '12.bg1.a1', '12.bg1.b1', '12.bh1.a1', '12.bh1.b1', '12.bi1.a1', '12.bi1.b1', '12.bj1.a1', '12.bk1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5500, -1, 4314, -1, 5539, -1, 4398, -1], 'generators': [339, 18, 12, 168], 'label': '384.18235.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66020935
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.i1.d1', '24.x1.a1'], 'contains': ['96.d2.a2', '96.f2.a2', '96.i1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3663, -1, 6379, -1, 4361, -1, 7085, -1], 'generators': [171, 18], 'label': '384.18235.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.b1', 'old_label': '48.m1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020936
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.i1.c1', '24.x1.b1'], 'contains': ['96.d2.a1', '96.f2.a1', '96.i1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3663, -1, 6555, -1, 4361, -1, 6136, -1], 'generators': [351, 18], 'label': '384.18235.48.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '48.m1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020937
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.e1.b1', '24.y1.a1'], 'contains': ['96.d1.a1', '96.f1.a1', '96.j1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3180, -1, 5250, -1, 3408, -1, 6518, -1], 'generators': [231, 18], 'label': '384.18235.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '48.n1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020938
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.f1.a1', '24.f1.b1'], 'contains': ['96.d1.a1', '96.d2.a1', '96.d2.a2', '96.n1.a1', '96.n1.a2', '96.n1.a3', '96.n1.a4'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1242, -1, 9114, -1, 1809, -1, 9252, -1], 'generators': [18, 12, 48], 'label': '384.18235.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.o1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020939
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.g1.b1', '24.bd1.a1'], 'contains': ['96.e2.a1', '96.f1.a1', '96.i1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3505, -1, 6101, -1, 4128, -1, 6762, -1], 'generators': [339, 180], 'label': '384.18235.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '48.p1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020940
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.g1.b1', '24.bd1.b1'], 'contains': ['96.e2.a2', '96.f1.a1', '96.i1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3505, -1, 6146, -1, 4128, -1, 6840, -1], 'generators': [345, 180], 'label': '384.18235.48.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '48.p1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020941
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.bg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.g1.b1', '24.bg1.a1'], 'contains': ['96.e1.a1', '96.i1.a1', '96.i1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3300, -1, 6211, -1, 3826, -1, 7198, -1], 'generators': [27, 180], 'label': '384.18235.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '48.q1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020942
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.g1.a1', '24.g1.b1'], 'contains': ['96.e1.a1', '96.e2.a1', '96.e2.a2', '96.o1.a1', '96.o1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1987, -1, 7017, -1, 2473, -1, 8014, -1], 'generators': [306, 132, 48], 'label': '384.18235.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '48.r1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020943
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.h1.b1', '24.bj1.a1'], 'contains': ['96.f2.a2', '96.g1.a1', '96.j1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6642, -1, 2160, -1, 8115, -1, 1306, -1], 'generators': [345, 168], 'label': '384.18235.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.s1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020944
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.bj1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.h1.b1', '24.bj1.b1'], 'contains': ['96.f2.a1', '96.g1.b1', '96.j1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6642, -1, 1633, -1, 8115, -1, 1777, -1], 'generators': [231, 174], 'label': '384.18235.48.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.s1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020945
    {'ambient': '384.18235', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6144.bkh', 'aut_weyl_index': 1, 'centralizer': '384.a1.a1', 'complements': ['192.b1.a1', '192.c1.a1', '192.c1.b1', '192.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '8.a1.a1', '8.b1.a1', '8.c1.a1', '8.c1.b1', '8.d1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3807, 3699, 7166, 3848, 932, 2363, 8806, 2275], 'generators': [2, 48, 96, 6, 192, 12, 24], 'label': '384.18235.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '384.18235'}
  • id: 66020946
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.a1.a1'], 'contains': ['24.a1.a1', '32.a1.a1', '32.b1.a1', '32.b1.a2', '32.b1.a3', '32.b1.a4'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [301, -1, 9524, -1, 296, -1, 9363, -1], 'generators': [2, 192, 6, 12, 48], 'label': '384.18235.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 66020947
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.h1.b1', '24.bk1.a1'], 'contains': ['96.f2.a1', '96.f2.a2', '96.h1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7173, -1, 1712, -1, 8531, -1, 2590, -1], 'generators': [39, 186], 'label': '384.18235.48.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.t1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020948
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.h1.b1', '24.bn1.a1'], 'contains': ['96.g1.a1', '96.g1.b1', '96.h1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7732, -1, 2837, -1, 8825, -1, 1171, -1], 'generators': [186, 336], 'label': '384.18235.48.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.u1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020949
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.n1.a1', '24.o1.a1', '24.o1.b1', '24.p1.a1', '24.p1.b1', '24.q1.a1', '24.q1.b1', '24.r1.a1', '24.r1.b1', '24.s1.a1', '24.s1.b1', '24.t1.a1', '24.u1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.c1.b1', '96.c2.a1', '96.c2.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3890, -1, 5542, -1, 4706, -1, 4965, -1], 'generators': [21, 48, 192], 'label': '384.18235.48.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.v1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020950
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.j1.a1', '24.u1.a1', '24.v1.a1', '24.v1.b1', '24.w1.a1', '24.x1.a1', '24.x1.b1', '24.y1.a1', '24.z1.a1', '24.z1.b1', '24.ba1.a1', '24.bb1.a1', '24.bb1.b1', '24.bc1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '96.d2.a1', '96.d2.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3090, -1, 6052, -1, 3650, -1, 6053, -1], 'generators': [18, 48, 192], 'label': '384.18235.48.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.w1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020951
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.k1.a1', '24.n1.a1', '24.o1.a1', '24.o1.b1', '24.v1.a1', '24.v1.b1', '24.w1.a1', '24.bd1.a1', '24.bd1.b1', '24.be1.a1', '24.be1.b1', '24.bf1.a1', '24.bg1.a1', '24.bh1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '96.e2.a1', '96.e2.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3752, -1, 5950, -1, 4003, -1, 5816, -1], 'generators': [180, 48, 192], 'label': '384.18235.48.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.x1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020952
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.n1.a1', '24.p1.a1', '24.p1.b1', '24.x1.a1', '24.x1.b1', '24.y1.a1', '24.bd1.a1', '24.bd1.b1', '24.bi1.a1', '24.bi1.b1', '24.bj1.a1', '24.bj1.b1', '24.bk1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '96.f2.a1', '96.f2.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4436, -1, 3873, -1, 5542, -1, 3741, -1], 'generators': [189, 48, 192], 'label': '384.18235.48.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.y1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020953
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.m1.a1', '24.p1.a1', '24.q1.a1', '24.r1.a1', '24.v1.a1', '24.z1.a1', '24.ba1.a1', '24.be1.a1', '24.bf1.a1', '24.bi1.a1', '24.bj1.a1', '24.bl1.a1', '24.bm1.a1', '24.bn1.a1'], 'contains': ['96.a1.a1', '96.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5582, -1, 4350, -1, 6310, -1, 2781, -1], 'generators': [168, 192], 'label': '384.18235.48.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.z1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020954
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '24.m1.b1', '24.p1.b1', '24.q1.b1', '24.r1.b1', '24.v1.b1', '24.z1.b1', '24.ba1.a1', '24.be1.b1', '24.bf1.a1', '24.bi1.b1', '24.bj1.b1', '24.bl1.b1', '24.bm1.b1', '24.bn1.a1'], 'contains': ['96.a1.a1', '96.g1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5582, -1, 2948, -1, 6310, -1, 3085, -1], 'generators': [174, 192], 'label': '384.18235.48.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.z1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020955
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.l1.a1', '24.s1.a1', '24.s1.b1', '24.t1.a1', '24.w1.a1', '24.z1.a1', '24.z1.b1', '24.be1.a1', '24.be1.b1', '24.bk1.a1', '24.bn1.a1', '24.bo1.a1', '24.bo1.b1', '24.bp1.a1'], 'contains': ['96.a1.a1', '96.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6484, -1, 3411, -1, 7674, -1, 4154, -1], 'generators': [186, 48], 'label': '384.18235.48.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.ba1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020956
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.o1.a1', '24.q1.b1', '24.s1.a1', '24.x1.a1', '24.bb1.a1', '24.bc1.a1', '24.bd1.a1', '24.bg1.a1', '24.bi1.b1', '24.bl1.b1', '24.bm1.a1', '24.bo1.a1', '24.bp1.a1'], 'contains': ['96.a1.a1', '96.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4857, -1, 4200, -1, 5365, -1, 5083, -1], 'generators': [171, 192], 'label': '384.18235.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bb1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020957
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['24.b1.a1', '32.a1.a1', '32.c1.a1', '32.c1.a2'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [663, -1, 8914, -1, 698, -1, 9150, -1], 'generators': [2, 192, 222, 180, 48], 'label': '384.18235.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 66020958
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '24.o1.b1', '24.q1.a1', '24.s1.b1', '24.x1.b1', '24.bb1.b1', '24.bc1.a1', '24.bd1.b1', '24.bg1.a1', '24.bi1.a1', '24.bl1.a1', '24.bm1.b1', '24.bo1.b1', '24.bp1.a1'], 'contains': ['96.a1.a1', '96.i1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4857, -1, 4970, -1, 5365, -1, 4813, -1], 'generators': [177, 192], 'label': '384.18235.48.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bb1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020959
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.r1.a1', '24.r1.b1', '24.t1.a1', '24.y1.a1', '24.bb1.a1', '24.bb1.b1', '24.bh1.a1', '24.bj1.a1', '24.bj1.b1', '24.bl1.a1', '24.bl1.b1', '24.bo1.a1', '24.bo1.b1'], 'contains': ['96.a1.a1', '96.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5741, -1, 3326, -1, 5732, -1, 3232, -1], 'generators': [183, 48], 'label': '384.18235.48.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bc1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66020960
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.f1.b1'], 'contains': ['96.k1.a1', '96.m1.a1', '96.n1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [748, -1, 9449, -1, 1482, -1, 9429, -1], 'generators': [3, 18, 12], 'label': '384.18235.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.bd1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66020961
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a2', '24.f1.b1'], 'contains': ['96.k1.a2', '96.m1.a1', '96.n1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [748, -1, 9331, -1, 1482, -1, 9518, -1], 'generators': [51, 66, 12], 'label': '384.18235.48.bd1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.bd1.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66020962
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.f1.a1'], 'contains': ['96.k1.b1', '96.m1.b1', '96.n1.a3'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [748, -1, 9062, -1, 1482, -1, 9607, -1], 'generators': [243, 210, 12], 'label': '384.18235.48.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.bd1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66020963
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b2', '24.f1.a1'], 'contains': ['96.k1.b2', '96.m1.b1', '96.n1.a4'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [748, -1, 9259, -1, 1482, -1, 9696, -1], 'generators': [195, 258, 12], 'label': '384.18235.48.bd1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.bd1.b2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.b2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66020964
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.bd2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.f1.b1'], 'contains': ['96.k1.a2', '96.k1.b1', '96.k1.b2', '96.m1.b1', '96.m2.a1', '96.m2.a2', '96.n1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [924, -1, 9011, -1, 1615, -1, 9163, -1], 'generators': [51, 18, 12], 'label': '384.18235.48.bd2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.bd2.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020965
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.bd2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.f1.b1'], 'contains': ['96.k1.a1', '96.k1.b1', '96.k1.b2', '96.m1.b1', '96.m2.a1', '96.m2.a2', '96.n1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [924, -1, 8793, -1, 1615, -1, 9341, -1], 'generators': [3, 66, 12], 'label': '384.18235.48.bd2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.bd2.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd2.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020966
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.bd2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.f1.b1'], 'contains': ['96.k1.a1', '96.k1.a2', '96.k1.b1', '96.m1.a1', '96.m2.a1', '96.m2.a2', '96.n1.a4'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [924, -1, 8844, -1, 1615, -1, 9074, -1], 'generators': [3, 258, 12], 'label': '384.18235.48.bd2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.bd2.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020967
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '48.bd2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.f1.b1'], 'contains': ['96.k1.a1', '96.k1.a2', '96.k1.b2', '96.m1.a1', '96.m2.a1', '96.m2.a2', '96.n1.a3'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [924, -1, 8926, -1, 1615, -1, 8985, -1], 'generators': [3, 210, 12], 'label': '384.18235.48.bd2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.bd2.b2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd2.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020968
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.1008', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.d1.a1'], 'contains': ['24.c1.a1', '32.a1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3501, -1, 8691, -1, 881, -1, 8637, -1], 'generators': [2, 192, 24, 96, 48], 'label': '384.18235.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.c1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.71'}
  • id: 66020969
    {'ambient': '384.18235', 'aut_centralizer_order': 48, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.a2', '16.b1.b1', '16.b1.b2'], 'contains': ['128.a1.a1', '192.b1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [583, -1, 9818, -1, 501, -1, 9817, -1], 'generators': [3, 2], 'label': '384.18235.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020970
    {'ambient': '384.18235', 'aut_centralizer_order': 1024, 'aut_label': '96.a1', 'aut_quo_index': 60, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '3.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.v1.a1', '48.w1.a1', '48.x1.a1', '48.y1.a1', '48.z1.a1', '48.z1.b1', '48.ba1.a1', '48.bb1.a1', '48.bb1.b1', '48.bc1.a1'], 'contains': ['192.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4016, 4084, 4971, 3948, 4706, 4411, 4965, 4125], 'generators': [48, 192], 'label': '384.18235.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 64, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.b1.a1', '24.a1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '48.a1.a1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': '3.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66020971
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '48.b2.a1', '48.b2.a2', '48.c1.a1', '48.d1.a1'], 'contains': ['192.a1.a1', '192.b1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2293, -1, 7758, -1, 2630, -1, 8541, -1], 'generators': [3, 48], 'label': '384.18235.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020972
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.e1.a1', '48.f1.a1', '48.f1.b1', '48.g1.a1', '48.g1.b1', '48.i1.a1', '48.j1.b1', '48.j1.b2', '48.v1.a1'], 'contains': ['192.a1.a1', '192.c1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2805, -1, 6128, -1, 3295, -1, 6780, -1], 'generators': [21, 240], 'label': '384.18235.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020973
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.b1', '48.e1.b1', '48.f1.c1', '48.f1.d1', '48.g1.c1', '48.g1.d1', '48.i1.b1', '48.j1.a1', '48.j1.a2', '48.v1.a1'], 'contains': ['192.a1.a1', '192.c1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2805, -1, 6075, -1, 3295, -1, 7189, -1], 'generators': [213, 240], 'label': '384.18235.96.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.c1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020974
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.c2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b2.a1', '48.e2.a2', '48.h1.b1', '48.j1.a2', '48.j1.b2', '48.j2.a1', '48.v1.a1'], 'contains': ['192.a1.a1', '192.c1.a1', '192.c1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2539, -1, 7353, -1, 2896, -1, 8274, -1], 'generators': [21, 192], 'label': '384.18235.96.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.c2.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020975
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.c2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b2.a2', '48.e2.a1', '48.h1.a1', '48.j1.a1', '48.j1.b1', '48.j2.a1', '48.v1.a1'], 'contains': ['192.a1.a1', '192.c1.a1', '192.c1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2539, -1, 7577, -1, 2896, -1, 8096, -1], 'generators': [21, 48], 'label': '384.18235.96.c2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.c2.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c2.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020976
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.b1.b1', '48.j2.a1', '48.l1.a1', '48.n1.a1', '48.o1.a1', '48.w1.a1'], 'contains': ['192.a1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1612, -1, 7638, -1, 2498, -1, 8452, -1], 'generators': [18, 240], 'label': '384.18235.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.d1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020977
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.d2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b2.a1', '48.j1.a1', '48.j1.b1', '48.k1.a1', '48.m1.b1', '48.o1.a1', '48.w1.a1'], 'contains': ['192.a1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2426, -1, 7853, -1, 2763, -1, 8185, -1], 'generators': [18, 192], 'label': '384.18235.96.d2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.d2.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020978
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.d2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b2.a2', '48.j1.a2', '48.j1.b2', '48.k1.b1', '48.m1.a1', '48.o1.a1', '48.w1.a1'], 'contains': ['192.a1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2426, -1, 7404, -1, 2763, -1, 8363, -1], 'generators': [18, 48], 'label': '384.18235.96.d2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.d2.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d2.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020979
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.1008', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.d1.b1'], 'contains': ['24.c1.b1', '32.a1.a1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3501, -1, 5187, -1, 881, -1, 8759, -1], 'generators': [2, 192, 366, 108, 48], 'label': '384.18235.8.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.b1', 'old_label': '8.c1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '96.71'}
  • id: 66020980
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.e1.a1', '48.e1.b1', '48.l1.a1', '48.q1.a1', '48.r1.a1', '48.x1.a1'], 'contains': ['192.a1.a1', '192.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2700, -1, 5780, -1, 3029, -1, 7669, -1], 'generators': [180, 192], 'label': '384.18235.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.e1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020981
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.e2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e2.a1', '48.f1.b1', '48.f1.d1', '48.k1.a1', '48.p1.a1', '48.r1.a1', '48.x1.a1'], 'contains': ['192.a1.a1', '192.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2923, -1, 6614, -1, 3428, -1, 6869, -1], 'generators': [180, 240], 'label': '384.18235.96.e2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '96.e2.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020982
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.e2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e2.a2', '48.f1.a1', '48.f1.c1', '48.k1.b1', '48.p1.b1', '48.r1.a1', '48.x1.a1'], 'contains': ['192.a1.a1', '192.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2923, -1, 6852, -1, 3428, -1, 7311, -1], 'generators': [180, 48], 'label': '384.18235.96.e2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '96.e2.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e2.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020983
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.e1.a1', '48.e1.b1', '48.n1.a1', '48.p1.a1', '48.p1.b1', '48.y1.a1'], 'contains': ['192.a1.a1', '192.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3088, -1, 5446, -1, 3560, -1, 7035, -1], 'generators': [189, 192], 'label': '384.18235.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.f1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020984
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.f2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e2.a1', '48.g1.a1', '48.g1.c1', '48.m1.b1', '48.s1.b1', '48.t1.a1', '48.y1.a1'], 'contains': ['192.a1.a1', '192.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4305, -1, 4873, -1, 5249, -1, 3001, -1], 'generators': [189, 240], 'label': '384.18235.96.f2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.b1', 'old_label': '96.f2.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020985
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.f2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e2.a2', '48.g1.b1', '48.g1.d1', '48.m1.a1', '48.s1.a1', '48.t1.a1', '48.y1.a1'], 'contains': ['192.a1.a1', '192.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4305, -1, 2899, -1, 5249, -1, 3741, -1], 'generators': [189, 48], 'label': '384.18235.96.f2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '96.f2.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f2.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020986
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.g1.c1', '48.h1.a1', '48.k1.a1', '48.s1.a1', '48.u1.a1', '48.z1.a1'], 'contains': ['192.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4977, -1, 4923, -1, 5900, -1, 2725, -1], 'generators': [168], 'label': '384.18235.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.b1', 'old_label': '96.g1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020987
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.b1', '48.g1.d1', '48.h1.b1', '48.k1.b1', '48.s1.b1', '48.u1.a1', '48.z1.b1'], 'contains': ['192.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4977, -1, 2948, -1, 5900, -1, 3085, -1], 'generators': [174], 'label': '384.18235.96.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '96.g1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020988
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.i1.a1', '48.i1.b1', '48.l1.a1', '48.t1.a1', '48.u1.a1', '48.ba1.a1'], 'contains': ['192.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6484, -1, 3409, -1, 7674, -1, 4080, -1], 'generators': [186], 'label': '384.18235.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '96.h1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020989
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.f1.c1', '48.h1.b1', '48.m1.a1', '48.p1.a1', '48.q1.a1', '48.bb1.a1'], 'contains': ['192.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3618, -1, 5923, -1, 4128, -1, 6952, -1], 'generators': [171], 'label': '384.18235.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '96.i1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020990
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.c1.a1'], 'contains': ['24.d1.a1', '32.a1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4562, -1, 5640, -1, 1198, -1, 8882, -1], 'generators': [2, 192, 150, 36, 48], 'label': '384.18235.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.d1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.72'}
  • id: 66020991
    {'ambient': '384.18235', 'aut_centralizer_order': 256, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.f1.d1', '48.h1.a1', '48.m1.b1', '48.p1.b1', '48.q1.a1', '48.bb1.b1'], 'contains': ['192.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3618, -1, 6027, -1, 4128, -1, 6488, -1], 'generators': [177], 'label': '384.18235.96.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '96.i1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020992
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.i1.a1', '48.i1.b1', '48.n1.a1', '48.s1.a1', '48.s1.b1', '48.bc1.a1'], 'contains': ['192.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5360, -1, 3278, -1, 4977, -1, 3931, -1], 'generators': [183], 'label': '384.18235.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '96.j1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66020993
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.b2.a1', '48.b2.a2', '48.bd1.a1', '48.bd2.a2', '48.bd2.b1', '48.bd2.b2'], 'contains': ['192.b1.a1', '192.c1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1146, -1, 8663, -1, 1966, -1, 8896, -1], 'generators': [3, 18], 'label': '384.18235.96.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.k1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020994
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.b2.a1', '48.b2.a2', '48.bd1.a2', '48.bd2.a1', '48.bd2.b1', '48.bd2.b2'], 'contains': ['192.b1.a1', '192.c1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1146, -1, 8964, -1, 1966, -1, 8985, -1], 'generators': [243, 18], 'label': '384.18235.96.k1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.k1.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020995
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.b1', '48.b2.a1', '48.b2.a2', '48.bd1.b1', '48.bd2.a1', '48.bd2.a2', '48.bd2.b1'], 'contains': ['192.b1.a1', '192.c1.b1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1146, -1, 8850, -1, 1966, -1, 9252, -1], 'generators': [195, 18], 'label': '384.18235.96.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.k1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020996
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.b1', '48.b2.a1', '48.b2.a2', '48.bd1.b2', '48.bd2.a1', '48.bd2.a2', '48.bd2.b2'], 'contains': ['192.b1.a1', '192.c1.b1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1146, -1, 8902, -1, 1966, -1, 9163, -1], 'generators': [51, 18], 'label': '384.18235.96.k1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.k1.b2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020997
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.e2.a1', '48.e2.a2'], 'contains': ['192.c1.a1', '192.e1.a1', '192.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1764, -1, 7138, -1, 3162, -1, 7581, -1], 'generators': [9, 180], 'label': '384.18235.96.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.l1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020998
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '48.e2.a1', '48.e2.a2'], 'contains': ['192.c1.b1', '192.e1.a1', '192.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1764, -1, 7086, -1, 3162, -1, 7758, -1], 'generators': [57, 180], 'label': '384.18235.96.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.l1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66020999
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.b1', '48.j1.b2', '48.j2.a1', '48.bd1.a1', '48.bd1.a2', '48.bd2.b1', '48.bd2.b2'], 'contains': ['192.c1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1241, -1, 8612, -1, 2099, -1, 8807, -1], 'generators': [15, 18], 'label': '384.18235.96.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.m1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021000
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.j1.a2', '48.j2.a1', '48.bd1.b1', '48.bd1.b2', '48.bd2.a1', '48.bd2.a2'], 'contains': ['192.c1.b1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1241, -1, 8449, -1, 2099, -1, 9074, -1], 'generators': [255, 18], 'label': '384.18235.96.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.m1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021001
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '12.a1.a1', 'complements': ['32.c1.a1', '32.c1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.f1.b1', '24.j1.a1', '24.u1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [390, 9441, 9009, 6394, 1039, 3657, 9257, 9581], 'generators': [3, 18, 12, 192, 48], 'label': '384.18235.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['24.a1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': '12.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66021002
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.m2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.j1.b2', '48.j2.a1', '48.bd2.a1', '48.bd2.a2', '48.bd2.b1', '48.bd2.b2'], 'contains': ['192.c1.a1', '192.c1.b1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1338, -1, 8372, -1, 2232, -1, 8718, -1], 'generators': [63, 18], 'label': '384.18235.96.m2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.m2.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021003
    {'ambient': '384.18235', 'aut_centralizer_order': 128, 'aut_label': '96.m2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a2', '48.j1.b1', '48.j2.a1', '48.bd2.a1', '48.bd2.a2', '48.bd2.b1', '48.bd2.b2'], 'contains': ['192.c1.a1', '192.c1.b1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1338, -1, 8311, -1, 2232, -1, 8629, -1], 'generators': [207, 18], 'label': '384.18235.96.m2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.m2.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m2.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021004
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.o1.a1', '48.bd1.a1', '48.bd2.a1'], 'contains': ['192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [880, -1, 9596, -1, 1615, -1, 9341, -1], 'generators': [18, 12], 'label': '384.18235.96.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '96.n1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66021005
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a2', '48.o1.a1', '48.bd1.a2', '48.bd2.a2'], 'contains': ['192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [880, -1, 9544, -1, 1615, -1, 9607, -1], 'generators': [66, 12], 'label': '384.18235.96.n1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '96.n1.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66021006
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a3', '48.o1.a1', '48.bd1.b1', '48.bd2.b2'], 'contains': ['192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [880, -1, 9355, -1, 1615, -1, 9429, -1], 'generators': [210, 12], 'label': '384.18235.96.n1.a3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '96.n1.a3', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a3', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66021007
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a4', '48.o1.a1', '48.bd1.b2', '48.bd2.b1'], 'contains': ['192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [880, -1, 9473, -1, 1615, -1, 9518, -1], 'generators': [258, 12], 'label': '384.18235.96.n1.a4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '96.n1.a4', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a4', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66021008
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.r1.a1'], 'contains': ['192.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1498, -1, 7240, -1, 2365, -1, 8007, -1], 'generators': [354, 180], 'label': '384.18235.96.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '96.o1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66021009
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a2', '48.r1.a1'], 'contains': ['192.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1498, -1, 7189, -1, 2365, -1, 7918, -1], 'generators': [306, 180], 'label': '384.18235.96.o1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '96.o1.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.a2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 66021010
    {'ambient': '384.18235', 'aut_centralizer_order': 48, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.b1.a2', '32.b1.a3', '32.b1.a4', '32.c1.a1', '32.c1.a2', '64.a1.a1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [583, -1, 9760, -1, 698, -1, 9821, -1], 'generators': [2], 'label': '384.18235.128.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021011
    {'ambient': '384.18235', 'aut_centralizer_order': 2048, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '96.c1.b1', '96.c2.a1', '96.c2.a2', '96.d1.a1', '96.d2.a1', '96.d2.a2', '96.e1.a1', '96.e2.a1', '96.e2.a2', '96.f1.a1', '96.f2.a1', '96.f2.a2', '96.g1.a1', '96.g1.b1', '96.h1.a1', '96.i1.a1', '96.i1.b1', '96.j1.a1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2937, -1, 6052, -1, 3428, -1, 7075, -1], 'generators': [48], 'label': '384.18235.192.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021012
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 16, 'centralizer': '96.a1.a1', 'complements': ['32.b1.a1', '32.b1.a4', '32.b1.a2', '32.b1.a3'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.d1.a1'], 'contains': ['24.b1.a1', '24.k1.a1', '24.bh1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1210, 5602, 7780, 9542, 1431, 7383, 8310, 4925], 'generators': [3, 354, 180], 'label': '384.18235.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['24.b1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': '12.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.229'}
  • id: 66021013
    {'ambient': '384.18235', 'aut_centralizer_order': 1536, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.b1.a1', '96.k1.a1', '96.k1.a2', '96.k1.b1', '96.k1.b2'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1201, -1, 8850, -1, 2041, -1, 8985, -1], 'generators': [3], 'label': '384.18235.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021014
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.c2.a1', '96.c2.a2', '96.k1.a1', '96.k1.a2', '96.l1.a1', '96.m1.a1', '96.m2.a1', '96.m2.a2'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1548, -1, 8292, -1, 2622, -1, 8590, -1], 'generators': [21], 'label': '384.18235.192.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '192.c1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021015
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.b1', '96.c2.a1', '96.c2.a2', '96.k1.b1', '96.k1.b2', '96.l1.b1', '96.m1.b1', '96.m2.a1', '96.m2.a2'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1548, -1, 8138, -1, 2622, -1, 8668, -1], 'generators': [69], 'label': '384.18235.192.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '192.c1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021016
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.d2.a1', '96.d2.a2', '96.k1.a1', '96.k1.a2', '96.k1.b1', '96.k1.b2', '96.m1.a1', '96.m1.b1', '96.m2.a1', '96.m2.a2', '96.n1.a1', '96.n1.a2', '96.n1.a3', '96.n1.a4'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1338, -1, 8632, -1, 2232, -1, 8901, -1], 'generators': [18], 'label': '384.18235.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '192.d1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021017
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.e2.a1', '96.e2.a2', '96.l1.a1', '96.l1.b1', '96.o1.a1', '96.o1.a2'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1764, -1, 7109, -1, 3029, -1, 7714, -1], 'generators': [180], 'label': '384.18235.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '192.e1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021018
    {'ambient': '384.18235', 'aut_centralizer_order': 512, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '96.f2.a1', '96.f2.a2', '96.l1.a1', '96.l1.b1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2636, -1, 5729, -1, 3552, -1, 6996, -1], 'generators': [189], 'label': '384.18235.192.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.m1.a1', 'old_label': '192.f1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021019
    {'ambient': '384.18235', 'aut_centralizer_order': None, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '192.a1.a1', '192.b1.a1', '192.c1.a1', '192.c1.b1', '192.d1.a1', '192.e1.a1', '192.f1.a1'], 'contains': [], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1548, 4084, 8209, 3948, 2622, 4411, 8629, 4125], 'generators': [], 'label': '384.18235.384.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '384.a1.a1', 'normal_contained_in': ['96.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021020
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 16, 'centralizer': '96.a1.a1', 'complements': ['32.c1.a2', '32.c1.a1', '32.b1.a1', '32.b1.a2', '32.b1.a4', '32.b1.a3'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.c1.a1'], 'contains': ['24.d1.a1', '24.l1.a1', '24.bk1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8810, 7924, 804, 7639, 9669, 9430, 6175, 3180], 'generators': [3, 186, 228], 'label': '384.18235.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['24.d1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '384.18235', 'quotient_action_image': '12.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.229'}
  • id: 66021021
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 32, 'centralizer': '96.a1.a1', 'complements': ['32.b1.a1', '32.b1.a3', '32.b1.a2', '32.b1.a4', '32.c1.a2', '32.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.b1'], 'contains': ['24.c1.a1', '24.m1.a1', '24.bm1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6856, 1099, 5675, 4993, 5743, 5166, 1122, 8295], 'generators': [3, 168, 336], 'label': '384.18235.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['24.c1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '384.18235', 'quotient_action_image': '12.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.229'}
  • id: 66021022
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 32, 'centralizer': '96.a1.a1', 'complements': ['32.b1.a1', '32.b1.a3', '32.b1.a2', '32.b1.a4', '32.c1.a2', '32.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.b1.a1'], 'contains': ['24.c1.b1', '24.m1.b1', '24.bm1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6856, 1099, 395, 1188, 5743, 5166, 2511, 6813], 'generators': [3, 234, 348], 'label': '384.18235.12.d1.b1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['24.c1.b1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '384.18235', 'quotient_action_image': '12.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '96.229'}
  • id: 66021040
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.b1', '6.g1.a1'], 'contains': ['24.o1.b1', '24.r1.a1', '24.t1.a1', '24.be1.a1', '24.bh1.a1', '24.bl1.a1', '24.bo1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8182, -1, 3905, -1, 8014, -1, 2680, -1], 'generators': [351, 354, 216], 'label': '384.18235.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021023
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408640849', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['128.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.f1.b1', '6.g1.a1', '6.h1.a1', '6.i1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5221, 5148, 4423, 5036, 5414, 4411, 4018, 4925], 'generators': [3, 18, 12, 336, 168], 'label': '384.18235.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '12.a1.a1', '12.c1.a1', '12.b1.a1', '12.d1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.229'}
  • id: 66021024
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.e1.a1', '24.e1.b1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '24.n1.a1', '24.t1.a1', '24.w1.a1', '24.y1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1608, -1, 6297, -1, 1956, -1, 8130, -1], 'generators': [3, 18, 228, 192], 'label': '384.18235.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021025
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.j1.a1', '24.k1.a1', '24.m1.a1', '24.o1.a1', '24.r1.a1', '24.v1.a1', '24.bb1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3236, -1, 6763, -1, 2507, -1, 7231, -1], 'generators': [3, 18, 336], 'label': '384.18235.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021026
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.j1.a1', '24.k1.a1', '24.m1.b1', '24.o1.b1', '24.r1.b1', '24.v1.b1', '24.bb1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3236, -1, 6543, -1, 2507, -1, 7419, -1], 'generators': [3, 18, 180], 'label': '384.18235.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021027
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.j1.a1', '24.l1.a1', '24.m1.a1', '24.p1.a1', '24.s1.a1', '24.x1.a1', '24.z1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4632, -1, 5255, -1, 6308, -1, 5842, -1], 'generators': [3, 18, 168], 'label': '384.18235.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021028
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.j1.a1', '24.l1.a1', '24.m1.b1', '24.p1.b1', '24.s1.b1', '24.x1.b1', '24.z1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4632, -1, 4092, -1, 6308, -1, 6031, -1], 'generators': [3, 18, 348], 'label': '384.18235.12.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021029
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.b1.b1', '6.e1.a1'], 'contains': ['24.j1.a1', '24.m1.a1', '24.m1.b1', '24.q1.a1', '24.q1.b1', '24.ba1.a1', '24.bc1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3446, -1, 6046, -1, 3902, -1, 5160, -1], 'generators': [3, 18, 216], 'label': '384.18235.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021030
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.k1.a1', '24.l1.a1', '24.m1.a1', '24.bd1.a1', '24.be1.a1', '24.bj1.a1', '24.bo1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6187, -1, 4002, -1, 6542, -1, 4848, -1], 'generators': [3, 354, 216], 'label': '384.18235.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021031
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.k1.a1', '24.l1.a1', '24.m1.b1', '24.bd1.b1', '24.be1.b1', '24.bj1.b1', '24.bo1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6187, -1, 3117, -1, 6542, -1, 5323, -1], 'generators': [3, 186, 348], 'label': '384.18235.12.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021032
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.b1.b1', '6.d1.a1'], 'contains': ['24.k1.a1', '24.m1.a1', '24.m1.b1', '24.bf1.a1', '24.bg1.a1', '24.bl1.a1', '24.bl1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4208, -1, 4706, -1, 4497, -1, 3521, -1], 'generators': [3, 354, 168], 'label': '384.18235.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021033
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.b1.b1', '6.c1.a1'], 'contains': ['24.l1.a1', '24.m1.a1', '24.m1.b1', '24.bi1.a1', '24.bi1.b1', '24.bn1.a1', '24.bp1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7422, -1, 2512, -1, 9082, -1, 2400, -1], 'generators': [3, 186, 336], 'label': '384.18235.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.k1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021034
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '16.a1.a1', '16.b1.a1', '16.b1.a2', '16.b1.b1', '16.b1.b2'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [350, -1, 9564, -1, 296, -1, 9430, -1], 'generators': [3, 192, 48, 2, 6, 12], 'label': '384.18235.4.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 66021035
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.f1.a1', '6.h1.a1'], 'contains': ['24.o1.a1', '24.p1.a1', '24.q1.b1', '24.bd1.a1', '24.bf1.a1', '24.bi1.b1', '24.bm1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4974, -1, 4885, -1, 5926, -1, 2043, -1], 'generators': [339, 354, 168], 'label': '384.18235.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.l1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021036
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.b1', '6.h1.a1'], 'contains': ['24.o1.b1', '24.p1.b1', '24.q1.a1', '24.bd1.b1', '24.bf1.a1', '24.bi1.a1', '24.bm1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4974, -1, 4268, -1, 5926, -1, 1921, -1], 'generators': [351, 354, 168], 'label': '384.18235.12.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.l1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021037
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '48.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.a1', '6.f1.b1'], 'contains': ['24.n1.a1', '24.r1.a1', '24.r1.b1', '24.bf1.a1', '24.bh1.a1', '24.bj1.a1', '24.bj1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5446, -1, 2776, -1, 5315, -1, 522, -1], 'generators': [15, 354, 168], 'label': '384.18235.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021038
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.b1', '6.h1.a1'], 'contains': ['24.n1.a1', '24.p1.a1', '24.s1.b1', '24.bd1.b1', '24.be1.a1', '24.bi1.a1', '24.bk1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6019, -1, 5933, -1, 8316, -1, 3097, -1], 'generators': [15, 354, 216], 'label': '384.18235.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021039
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.h1.a1'], 'contains': ['24.n1.a1', '24.p1.b1', '24.s1.a1', '24.bd1.a1', '24.be1.b1', '24.bi1.b1', '24.bk1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6019, -1, 1469, -1, 8316, -1, 4050, -1], 'generators': [171, 186, 348], 'label': '384.18235.12.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021041
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.o1.a1', '24.r1.b1', '24.t1.a1', '24.be1.b1', '24.bh1.a1', '24.bl1.b1', '24.bo1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8182, -1, 1982, -1, 8014, -1, 2895, -1], 'generators': [219, 186, 348], 'label': '384.18235.12.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021042
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.bb1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.g1.a1', '6.h1.a1'], 'contains': ['24.o1.a1', '24.q1.a1', '24.s1.a1', '24.be1.a1', '24.bg1.a1', '24.bm1.a1', '24.bp1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6332, -1, 5080, -1, 7438, -1, 4983, -1], 'generators': [339, 354, 216], 'label': '384.18235.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021043
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.g1.a1', '6.h1.a1'], 'contains': ['24.o1.b1', '24.q1.b1', '24.s1.b1', '24.be1.b1', '24.bg1.a1', '24.bm1.b1', '24.bp1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6332, -1, 4471, -1, 7438, -1, 5459, -1], 'generators': [339, 186, 348], 'label': '384.18235.12.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021044
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '48.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.h1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '24.g1.b1', '24.n1.a1', '24.o1.a1', '24.o1.b1', '24.bd1.a1', '24.bd1.b1', '24.bg1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1809, -1, 8018, -1, 1700, -1, 8490, -1], 'generators': [171, 354, 180, 192], 'label': '384.18235.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.q1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021045
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.5678', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.b1.a1', '12.b1.a1', '16.a1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [621, -1, 8809, -1, 675, -1, 9086, -1], 'generators': [3, 192, 240, 2, 222, 180], 'label': '384.18235.4.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '4.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 66021046
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.f1.b1'], 'contains': ['24.c1.a1', '24.p1.a1', '24.q1.a1', '24.r1.a1', '24.bi1.a1', '24.bj1.a1', '24.bl1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7856, -1, 4190, -1, 7216, -1, 245, -1], 'generators': [21, 168, 336], 'label': '384.18235.12.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.r1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021047
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.z1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.a1'], 'contains': ['24.c1.b1', '24.p1.b1', '24.q1.b1', '24.r1.b1', '24.bi1.b1', '24.bj1.b1', '24.bl1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7856, -1, 178, -1, 7216, -1, 987, -1], 'generators': [171, 234, 348], 'label': '384.18235.12.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.r1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021048
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '48.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.f1.b1'], 'contains': ['24.h1.a1', '24.h1.b1', '24.p1.a1', '24.p1.b1', '24.t1.a1', '24.bj1.a1', '24.bj1.b1', '24.bk1.a1', '24.bn1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9732, -1, 46, -1, 9879, -1, 81, -1], 'generators': [231, 186, 336, 48], 'label': '384.18235.12.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.s1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021049
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.q1.b1', '24.r1.a1', '24.s1.a1', '24.bl1.b1', '24.bm1.a1', '24.bn1.a1', '24.bo1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8583, -1, 2215, -1, 8915, -1, 1583, -1], 'generators': [219, 186, 336], 'label': '384.18235.12.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021050
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.b1', '6.g1.a1'], 'contains': ['24.q1.a1', '24.r1.b1', '24.s1.b1', '24.bl1.a1', '24.bm1.b1', '24.bn1.a1', '24.bo1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8583, -1, 1756, -1, 8915, -1, 1460, -1], 'generators': [15, 186, 336], 'label': '384.18235.12.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021051
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '48.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.g1.a1'], 'contains': ['24.d1.a1', '24.s1.a1', '24.s1.b1', '24.t1.a1', '24.bo1.a1', '24.bo1.b1', '24.bp1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9932, -1, 2099, -1, 9450, -1, 4241, -1], 'generators': [171, 186, 228], 'label': '384.18235.12.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021052
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.b1', '6.h1.a1'], 'contains': ['24.i1.a1', '24.i1.c1', '24.n1.a1', '24.o1.b1', '24.p1.a1', '24.q1.a1', '24.u1.a1', '24.v1.a1', '24.x1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2842, -1, 8272, -1, 3058, -1, 7787, -1], 'generators': [15, 18, 336, 48], 'label': '384.18235.12.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021053
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.a1', '6.h1.a1'], 'contains': ['24.i1.b1', '24.i1.d1', '24.n1.a1', '24.o1.a1', '24.p1.b1', '24.q1.b1', '24.u1.a1', '24.v1.b1', '24.x1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2842, -1, 8118, -1, 3058, -1, 7959, -1], 'generators': [171, 18, 180, 192], 'label': '384.18235.12.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021054
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.g1.a1', '6.h1.a1'], 'contains': ['24.o1.a1', '24.o1.b1', '24.s1.a1', '24.s1.b1', '24.u1.a1', '24.w1.a1', '24.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2447, -1, 7432, -1, 3327, -1, 7608, -1], 'generators': [219, 18, 228], 'label': '384.18235.12.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021055
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.a1', '6.f1.b1'], 'contains': ['24.p1.a1', '24.p1.b1', '24.r1.a1', '24.r1.b1', '24.u1.a1', '24.y1.a1', '24.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3859, -1, 3503, -1, 4196, -1, 818, -1], 'generators': [15, 18, 216], 'label': '384.18235.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021056
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.d1.a1', '12.c1.a1', '16.a1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4401, -1, 5344, -1, 1307, -1, 8908, -1], 'generators': [3, 192, 48, 2, 150, 36], 'label': '384.18235.4.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '4.c1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.72'}
  • id: 66021057
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.b1', '6.g1.a1'], 'contains': ['24.q1.a1', '24.r1.a1', '24.s1.b1', '24.t1.a1', '24.u1.a1', '24.z1.a1', '24.bb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7259, -1, 5488, -1, 7702, -1, 3854, -1], 'generators': [15, 18, 168], 'label': '384.18235.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021058
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.q1.b1', '24.r1.b1', '24.s1.a1', '24.t1.a1', '24.u1.a1', '24.z1.b1', '24.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7259, -1, 2953, -1, 7702, -1, 4562, -1], 'generators': [339, 18, 348], 'label': '384.18235.12.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021059
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.b1', '6.i1.a1'], 'contains': ['24.v1.a1', '24.y1.a1', '24.bb1.b1', '24.bd1.b1', '24.bh1.a1', '24.bj1.a1', '24.bl1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5621, -1, 4550, -1, 5560, -1, 4398, -1], 'generators': [231, 18, 336], 'label': '384.18235.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021060
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.a1', '6.i1.a1'], 'contains': ['24.v1.b1', '24.y1.a1', '24.bb1.a1', '24.bd1.a1', '24.bh1.a1', '24.bj1.b1', '24.bl1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5621, -1, 2591, -1, 5560, -1, 4725, -1], 'generators': [339, 18, 180], 'label': '384.18235.12.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021061
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.v1.a1', '24.x1.a1', '24.bc1.a1', '24.bd1.a1', '24.bg1.a1', '24.bi1.a1', '24.bm1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4027, -1, 6142, -1, 4750, -1, 6386, -1], 'generators': [219, 18, 336], 'label': '384.18235.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021062
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.v1.b1', '24.x1.b1', '24.bc1.a1', '24.bd1.b1', '24.bg1.a1', '24.bi1.b1', '24.bm1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4027, -1, 6212, -1, 4750, -1, 6509, -1], 'generators': [219, 18, 180], 'label': '384.18235.12.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021063
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.w1.a1', '24.x1.a1', '24.x1.b1', '24.bd1.a1', '24.bd1.b1', '24.bk1.a1', '24.bp1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5283, -1, 5849, -1, 6709, -1, 6275, -1], 'generators': [171, 18, 228], 'label': '384.18235.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bb1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021064
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.g1.a1'], 'contains': ['24.d1.a1', '24.w1.a1', '24.z1.a1', '24.z1.b1', '24.be1.a1', '24.be1.b1', '24.bn1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8703, -1, 2865, -1, 9231, -1, 3364, -1], 'generators': [18, 348, 168], 'label': '384.18235.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021065
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.f1.a1'], 'contains': ['24.c1.b1', '24.v1.b1', '24.z1.b1', '24.ba1.a1', '24.be1.b1', '24.bf1.a1', '24.bn1.a1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6465, -1, 1891, -1, 6093, -1, 673, -1], 'generators': [18, 348, 216], 'label': '384.18235.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021066
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.b1', '6.f1.b1'], 'contains': ['24.c1.a1', '24.v1.a1', '24.z1.a1', '24.ba1.a1', '24.be1.a1', '24.bf1.a1', '24.bn1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6465, -1, 4615, -1, 6093, -1, 370, -1], 'generators': [18, 168, 336], 'label': '384.18235.12.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021067
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.1008', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.c1.a1', '12.d1.a1', '16.a1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3984, -1, 8711, -1, 1054, -1, 8536, -1], 'generators': [3, 192, 48, 2, 24, 96], 'label': '384.18235.4.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '4.d1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.71'}
  • id: 66021068
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.g1.a1', '6.i1.a1'], 'contains': ['24.w1.a1', '24.bb1.a1', '24.bb1.b1', '24.bg1.a1', '24.bh1.a1', '24.bo1.a1', '24.bo1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5802, -1, 4367, -1, 5002, -1, 5641, -1], 'generators': [339, 18, 228], 'label': '384.18235.12.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.be1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021069
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.h1.a1'], 'contains': ['24.b1.a1', '24.v1.a1', '24.v1.b1', '24.w1.a1', '24.be1.a1', '24.be1.b1', '24.bf1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3035, -1, 6401, -1, 2789, -1, 6665, -1], 'generators': [18, 180, 336], 'label': '384.18235.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bf1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021070
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.f1.a1', '6.i1.a1'], 'contains': ['24.x1.a1', '24.ba1.a1', '24.bb1.a1', '24.bi1.b1', '24.bj1.a1', '24.bl1.b1', '24.bm1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6651, -1, 1658, -1, 6943, -1, 1752, -1], 'generators': [339, 18, 216], 'label': '384.18235.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bg1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021071
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.b1', '6.i1.a1'], 'contains': ['24.x1.b1', '24.ba1.a1', '24.bb1.b1', '24.bi1.a1', '24.bj1.b1', '24.bl1.a1', '24.bm1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6651, -1, 3328, -1, 6943, -1, 1291, -1], 'generators': [351, 18, 216], 'label': '384.18235.12.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bg1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021072
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.b1', '6.i1.a1'], 'contains': ['24.x1.b1', '24.y1.a1', '24.z1.a1', '24.bi1.a1', '24.bj1.a1', '24.bk1.a1', '24.bo1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8001, -1, 1560, -1, 8732, -1, 2166, -1], 'generators': [351, 18, 168], 'label': '384.18235.12.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bh1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021073
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.i1.a1'], 'contains': ['24.x1.a1', '24.y1.a1', '24.z1.b1', '24.bi1.b1', '24.bj1.b1', '24.bk1.a1', '24.bo1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8001, -1, 869, -1, 8732, -1, 2288, -1], 'generators': [171, 18, 348], 'label': '384.18235.12.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bh1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021074
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '6.g1.a1', '6.i1.a1'], 'contains': ['24.z1.a1', '24.bb1.a1', '24.bc1.a1', '24.bl1.a1', '24.bm1.a1', '24.bo1.a1', '24.bp1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8363, -1, 3705, -1, 8549, -1, 3253, -1], 'generators': [339, 18, 168], 'label': '384.18235.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bi1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021075
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.g1.a1', '6.i1.a1'], 'contains': ['24.z1.b1', '24.bb1.b1', '24.bc1.a1', '24.bl1.b1', '24.bm1.b1', '24.bo1.b1', '24.bp1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8363, -1, 1826, -1, 8549, -1, 3690, -1], 'generators': [219, 18, 348], 'label': '384.18235.12.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bi1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 66021076
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.e1.a1', '6.i1.a1'], 'contains': ['24.a1.a1', '24.v1.a1', '24.v1.b1', '24.w1.a1', '24.z1.a1', '24.z1.b1', '24.ba1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2648, -1, 6652, -1, 2225, -1, 6853, -1], 'generators': [18, 12, 168], 'label': '384.18235.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bj1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021077
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.i1.a1'], 'contains': ['24.a1.a1', '24.x1.a1', '24.x1.b1', '24.y1.a1', '24.bb1.a1', '24.bb1.b1', '24.bc1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3657, -1, 5766, -1, 3609, -1, 7042, -1], 'generators': [171, 18, 12], 'label': '384.18235.12.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bk1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66021078
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.1008', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.c1.b1', '12.d1.b1', '16.a1.a1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3984, -1, 5189, -1, 1054, -1, 8698, -1], 'generators': [3, 192, 48, 2, 366, 108], 'label': '384.18235.4.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.b1', 'old_label': '4.d1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '96.71'}
  • id: 66021079
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.d1.b1'], 'contains': ['32.a1.a1', '48.a1.a1', '64.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [580, -1, 8835, -1, 497, -1, 9016, -1], 'generators': [3, 2, 48, 192], 'label': '384.18235.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66021080
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['32.b1.a1', '48.bd1.a1', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '16T731', 'count': 16, 'diagramx': [68, -1, 9909, -1, 95, -1, 9498, -1], 'generators': [3, 2, 18, 12], 'label': '384.18235.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '16.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66021081
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['32.b1.a2', '48.bd1.a2', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '16T731', 'count': 16, 'diagramx': [68, -1, 9824, -1, 95, -1, 9643, -1], 'generators': [3, 2, 258, 60], 'label': '384.18235.16.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '16.b1.a2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66021082
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['32.b1.a3', '48.bd1.b1', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '16T731', 'count': 16, 'diagramx': [68, -1, 9580, -1, 95, -1, 9790, -1], 'generators': [3, 2, 66, 204], 'label': '384.18235.16.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '16.b1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66021083
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['32.b1.a4', '48.bd1.b2', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': '16T731', 'count': 16, 'diagramx': [68, -1, 9716, -1, 95, -1, 9936, -1], 'generators': [3, 2, 210, 252], 'label': '384.18235.16.b1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '16.b1.b2', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66021084
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.bj1.a1', '12.bk1.a1'], 'contains': ['48.o1.a1', '48.w1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [890, 5515, 8711, 3347, 1657, 1886, 8855, 5738], 'generators': [18, 12, 48, 192], 'label': '384.18235.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -4, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1', '12.a1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': '12.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 66021085
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '24.b1.a1', 'complements': ['16.b1.a2', '16.b1.a1', '16.b1.b2', '16.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1', '12.q1.a1', '12.bf1.a1'], 'contains': ['48.r1.a1', '48.x1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1655, 2653, 6965, 5694, 1790, 4411, 8397, 2512], 'generators': [354, 180, 48, 192], 'label': '384.18235.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': -4, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['6.a1.a1', '12.b1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '384.18235', 'quotient_action_image': '24.13', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66021086
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '48.49', 'aut_weyl_index': 128, 'centralizer': '24.c1.a1', 'complements': ['16.b1.a1', '16.b1.a2', '16.b1.b2', '16.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1', '12.r1.a1', '12.bd1.b1'], 'contains': ['48.z1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6598, 559, 5586, 2174, 5897, 3149, 705, 4662], 'generators': [168, 336], 'label': '384.18235.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': -4, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['6.a1.a1', '12.d1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '384.18235', 'quotient_action_image': '24.13', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66021087
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '48.49', 'aut_weyl_index': 128, 'centralizer': '24.c1.b1', 'complements': ['16.b1.a1', '16.b1.b1', '16.b1.a2', '16.b1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.d1.b1', '12.r1.b1', '12.bd1.a1'], 'contains': ['48.z1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6598, 559, 1507, 458, 5897, 3149, 1799, 3587], 'generators': [234, 348], 'label': '384.18235.24.c1.b1', 'mobius_quo': 0, 'mobius_sub': -4, 'normal_closure': '24.c1.b1', 'normal_contained_in': ['6.a1.a1', '12.d1.b1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.b1', 'projective_image': '384.18235', 'quotient_action_image': '24.13', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66021088
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '24.d1.a1', 'complements': ['16.b1.a1', '16.b1.a2', '16.b1.b2', '16.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.c1.a1', '12.u1.a1', '12.bc1.a1'], 'contains': ['48.ba1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9072, 4084, 2043, 4520, 9181, 5674, 5253, 1436], 'generators': [186, 228], 'label': '384.18235.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': -4, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['6.a1.a1', '12.c1.a1'], 'normal_contains': ['96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '384.18235', 'quotient_action_image': '24.13', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 66021089
    {'ambient': '384.18235', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408640849', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['64.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.bc1.a1', '12.bd1.a1', '12.bd1.b1', '12.bf1.a1', '12.bj1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4943, 3316, 4829, 3305, 5015, 1440, 3488, 1226], 'generators': [18, 12, 168, 336], 'label': '384.18235.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['24.b1.a1', '24.a1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '384.18235', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.229'}
  • id: 66021090
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1'], 'contains': ['48.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.i1.a1', '48.l1.a1', '48.n1.a1'], 'core': '384.a1.a1', 'coset_action_label': '24T997', 'count': 12, 'diagramx': [2031, -1, 6180, -1, 2233, -1, 8130, -1], 'generators': [3, 18, 228], 'label': '384.18235.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '24.e1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66021091
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1'], 'contains': ['48.b1.b1', '48.c1.a1', '48.d1.a1', '48.e1.b1', '48.i1.b1', '48.l1.a1', '48.n1.a1'], 'core': '384.a1.a1', 'coset_action_label': '24T997', 'count': 12, 'diagramx': [2031, -1, 6266, -1, 2233, -1, 8278, -1], 'generators': [195, 18, 228], 'label': '384.18235.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '24.e1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66021092
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.b1.b1', '48.b2.a1', '48.b2.a2', '48.j1.a1', '48.j1.a2', '48.j2.a1', '48.o1.a1', '48.bd1.b1', '48.bd1.b2', '48.bd2.a1', '48.bd2.a2', '48.bd2.b1', '48.bd2.b2'], 'core': '384.a1.a1', 'coset_action_label': '24T730', 'count': 12, 'diagramx': [778, -1, 8818, -1, 1462, -1, 9267, -1], 'generators': [195, 18, 12, 48], 'label': '384.18235.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021093
    {'ambient': '384.18235', 'aut_centralizer_order': 64, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.b1.a1', '48.b2.a1', '48.b2.a2', '48.j1.b1', '48.j1.b2', '48.j2.a1', '48.o1.a1', '48.bd1.a1', '48.bd1.a2', '48.bd2.a1', '48.bd2.a2', '48.bd2.b1', '48.bd2.b2'], 'core': '384.a1.a1', 'coset_action_label': '24T730', 'count': 12, 'diagramx': [778, -1, 8973, -1, 1462, -1, 9178, -1], 'generators': [3, 18, 12, 48], 'label': '384.18235.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.f1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66021094
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.f1.b1', '48.p1.a1', '48.p1.b1', '48.q1.a1', '48.r1.a1'], 'core': '384.a1.a1', 'coset_action_label': '24T983', 'count': 12, 'diagramx': [2189, -1, 7062, -1, 2455, -1, 7685, -1], 'generators': [171, 354, 180], 'label': '384.18235.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '24.g1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66021095
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1'], 'contains': ['48.e1.b1', '48.f1.c1', '48.f1.d1', '48.p1.a1', '48.p1.b1', '48.q1.a1', '48.r1.a1'], 'core': '384.a1.a1', 'coset_action_label': '24T983', 'count': 12, 'diagramx': [2189, -1, 7158, -1, 2455, -1, 8558, -1], 'generators': [363, 354, 180], 'label': '384.18235.24.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '24.g1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66021096
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1'], 'contains': ['48.g1.a1', '48.g1.b1', '48.i1.a1', '48.s1.a1', '48.s1.b1', '48.t1.a1', '48.u1.a1'], 'core': '384.a1.a1', 'coset_action_label': '24T1025', 'count': 12, 'diagramx': [9174, -1, 1451, -1, 9322, -1, 511, -1], 'generators': [39, 186, 336], 'label': '384.18235.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '24.h1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66021097
    {'ambient': '384.18235', 'aut_centralizer_order': 16, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1'], 'contains': ['48.g1.c1', '48.g1.d1', '48.i1.b1', '48.s1.a1', '48.s1.b1', '48.t1.a1', '48.u1.a1'], 'core': '384.a1.a1', 'coset_action_label': '24T1025', 'count': 12, 'diagramx': [9174, -1, 1394, -1, 9322, -1, 611, -1], 'generators': [87, 186, 336], 'label': '384.18235.24.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '24.h1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66021098
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1'], 'contains': ['48.e2.a1', '48.f1.d1', '48.g1.c1', '48.h1.a1', '48.j1.a1', '48.k1.a1', '48.m1.b1'], 'core': '384.a1.a1', 'coset_action_label': '24T1024', 'count': 12, 'diagramx': [2349, -1, 7817, -1, 2899, -1, 7446, -1], 'generators': [63, 18, 336], 'label': '384.18235.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '24.i1.a1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66021099
    {'ambient': '384.18235', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.b1'], 'contains': ['48.e2.a2', '48.f1.c1', '48.g1.d1', '48.h1.b1', '48.j1.a2', '48.k1.b1', '48.m1.a1'], 'core': '384.a1.a1', 'coset_action_label': '24T1024', 'count': 12, 'diagramx': [2349, -1, 7340, -1, 2899, -1, 7982, -1], 'generators': [363, 18, 180], 'label': '384.18235.24.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.b1', 'old_label': '24.i1.b1', 'projective_image': '384.18235', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}