Abstract group data - 6144.ze

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 4, 12, 8, 6, 12, 6, 6], 'aut_gens': [[5167, 369690041928377, 377740048764960017, 134021272934136536501057, 216288449188486422410880], [5167, 432525928714315155825840, 25903364133006332144062, 162121668865829307105862, 486478219374380630085262], [25903229681844523008000, 350258631166442328422520, 79804173674311971067447, 54003382335836237186622, 458326732861803506399878], [25903229681844523008000, 458326854509714521632120, 377740048764960017, 54003503625249257476537, 296092878602059066763662], [5167, 594596384985952168278353, 79804051675006077619217, 162121668865829307100937, 566495988686051434617599], [25903229681844523008000, 540592881369105245172343, 54003247880382134979262, 79804308131248057039417, 242140587582181736447878], [25903229681844523008000, 620397310781363988131158, 25903485425202744014647, 79804308131248057039417, 404210921847430903862262], [1313941668480, 378358905102939341244720, 25903485425202744014647, 187973685956283861738823, 324406735725372938305912], [25903229681844523008000, 540593002658518185623743, 79804051675006077619217, 79804308129765938651519, 270240861511785222772553]], 'aut_group': '10000.cv', 'aut_hash': 4880800731101327399, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49152, 'aut_permdeg': 128, 'aut_perms': [159694909417647449617805926406138255352461334460289137417179264330572417182216888973887936935073134868393501291553134986220730826890409512729128219094784974399292127661161129840134590022031967752176919378777915153917, 345331989309734587548693164806555741216549508055684750940496951380542122270995336616725195649243233508218260213632905822634995191799274144999141775174634557786505813436490656668858644757340726936094227195902007710635, 61783129255367878014093312935423859408772993704521863243061917963725776162043566793604966826079999418318407668907685845143573996912413410844371170953518058737819480247438508347757172478264206748512602791286406697074, 342630537901959346018791180489034319837800627295940348559258407275925988200615791923018665612359505768693920516850642115266065356397973492071355537930200210382946071718452154593540142920672041432713190888944125564001, 203691744882804683030641644017642795973737231802453439929125556253764047851065937711065564689673882761421017612132353110920201630881394209645452935312905671450154196603285872737731614625120539336617088300056929176949, 377498739517817748271192743311135134180074074857418682201735959702472566737307603626893866990717745882262619025007147196060237303111054517273380273052732923527191181650747094293518025869806431903567852409160158324428, 170879818999839247190913718426095898137351078117868326318310105027063879978538819491097070849203097708691379851146603923282637792520337877021498199031503437718621390231252744536325550131290561303222165697265958414073, 257032309439117247308844805194818175918389133681679682129512649988040106410440342750058662691830115628680828033982067819007356935085808386398408359417220892204319109405026775074204810005120363767417400274978595873405], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 1, 2], [2, 8, 2, 1], [2, 12, 4, 1], [2, 24, 1, 4], [2, 24, 2, 1], [2, 24, 4, 1], [2, 32, 2, 1], [2, 48, 2, 2], [3, 128, 1, 1], [4, 6, 1, 4], [4, 8, 2, 1], [4, 12, 1, 2], [4, 24, 1, 4], [4, 24, 2, 2], [4, 24, 4, 1], [4, 48, 2, 3], [4, 96, 2, 1], [4, 96, 4, 2], [4, 192, 2, 1], [6, 128, 1, 3], [6, 256, 2, 2], [8, 48, 4, 3], [8, 96, 2, 3], [8, 192, 2, 1], [12, 256, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_5^3\\times C_{10}).Q_8', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 2330610246365708940, 'autcentquo_nilpotent': False, 'autcentquo_order': 6144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_4^2.(D_4\\times S_4).C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 4, 2], [2, 8, 2], [2, 12, 4], [2, 24, 10], [2, 32, 2], [2, 48, 4], [3, 128, 1], [4, 6, 4], [4, 8, 2], [4, 12, 2], [4, 24, 12], [4, 48, 6], [4, 96, 10], [4, 192, 2], [6, 128, 3], [6, 256, 4], [8, 48, 12], [8, 96, 6], [8, 192, 2], [12, 256, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '3072.bgb', 'commutator_count': 1, 'commutator_label': '384.18236', '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', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 655, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3072.bgb', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 1, 2], [2, 8, 1, 2], [2, 12, 1, 4], [2, 24, 1, 10], [2, 32, 1, 2], [2, 48, 1, 4], [3, 128, 1, 1], [4, 6, 1, 4], [4, 8, 1, 2], [4, 12, 1, 2], [4, 24, 1, 12], [4, 48, 1, 6], [4, 96, 1, 10], [4, 192, 1, 2], [6, 128, 1, 3], [6, 256, 1, 4], [8, 48, 1, 12], [8, 96, 1, 6], [8, 192, 1, 2], [12, 256, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 24, 'exponents_of_order': [11, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 8], [24, 1, 2]], 'familial': False, 'frattini_label': '32.21', 'frattini_quotient': '192.1537', 'hash': 4158378184127417885, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 4, 4, 4, 6], 'inner_gens': [[5167, 371003982865942, 377740048764960017, 134021272934136536501057, 216288449189800283525167], [1313941668480, 369690041928377, 256450635744670102, 133970182340738306169473, 486478098089065076203567], [5167, 121659103062218302, 377740048764960017, 162121547576416365923777, 216288570477899362867207], [5167, 51090961780558017359, 79804051675006077619217, 134021272934136536501057, 296041666020386996142598], [25903229681844523008000, 512330236124472161193622, 256450635744670102, 79804308129765938646352, 216288449188486422410880]], 'inner_hash': 7983714371117797868, 'inner_nilpotent': False, 'inner_order': 3072, 'inner_split': None, 'inner_tex': 'C_4^3:(C_2\\times S_4)', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 16], [2, 12], [3, 16], [4, 2], [6, 28], [12, 18], [24, 4]], 'label': '6144.ze', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C4^3:(C2^2*S4)', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 52, 'number_characteristic_subgroups': 46, 'number_conjugacy_classes': 96, 'number_divisions': 96, 'number_normal_subgroups': 126, 'number_subgroup_autclasses': 8176, 'number_subgroup_classes': 22034, 'number_subgroups': 397412, 'old_label': None, 'order': 6144, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 575], [3, 128], [4, 1984], [6, 1408], [8, 1536], [12, 512]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [122000787877212840, 122002101738321960, 432525928350198472081936, 566496110692445545802177], 'outer_gens': [[5167, 432525928714315155825840, 25903364133006332144062, 162121668865829307105862, 486478219374380630085262], [25903229681844523008000, 350258631166442328422520, 79804173674311971067447, 54003382335836237186622, 458326732861803506399878], [25903229681844523008000, 458326854509714521632120, 377740048764960017, 54003503625249257476537, 296092878602059066763662], [25903229681844523008000, 540592881369105245172343, 54003247880382134979262, 79804308131248057039417, 242140587582181736447878]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 16, 'outer_perms': [1327912203241, 2966658509284, 4396538203938, 5800737348096], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [3, 16], [4, 2], [6, 28], [12, 18], [24, 4]], 'representations': {'PC': {'code': '1614372118149799813814748845874373883761234298927647071458384247669894317222096881983923516752579442428514638772992058596956093255874654916674097690633747580401526930492133385884375101952', 'gens': [1, 2, 4, 6, 7, 8, 10, 12], 'pres': [12, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18432, 45169, 61, 71138, 1731, 2031, 22635, 135, 12256, 29188, 134789, 79505, 33725, 641, 374982, 191538, 85710, 3738, 1734, 906, 566791, 184339, 96799, 5035, 2359, 1219, 2191, 283, 207368, 82964, 51872, 311049, 80661, 109473, 10605, 11577, 6789, 2961, 357, 126742, 12706, 248855, 179747]}, 'Perm': {'d': 24, 'gens': [216288449188486422410880, 5167, 369690041928377, 134021272934136536501057, 377740048764960017]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 32, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_4^3:(C_2^2\\times S_4)', 'transitive_degree': 24, '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: 165012275
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 655, 'group_order': 6144, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 165012286
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 655, 'group_order': 6144, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 25903229683158464681647, 'size': 1}
  • id: 165012297
    {'aut_label': '2B', 'centralizer': '3.a1', 'counter': 3, 'group_counter': 655, 'group_order': 6144, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 5167, 'size': 3}
  • id: 165012308
    {'aut_label': '2C', 'centralizer': '3.a1', 'counter': 4, 'group_counter': 655, 'group_order': 6144, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 1313941673647, 'size': 3}
  • id: 165012319
    {'aut_label': '2D', 'centralizer': '4.O', 'counter': 5, 'group_counter': 655, 'group_order': 6144, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 122000787877207687, 'size': 4}
  • id: 165012330
    {'aut_label': '2E', 'centralizer': '4.O', 'counter': 6, 'group_counter': 655, 'group_order': 6144, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 25903107681056726359687, 'size': 4}
  • id: 165012341
    {'aut_label': '2F', 'centralizer': '8.K', 'counter': 7, 'group_counter': 655, 'group_order': 6144, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 51212587278385214641, 'size': 8}
  • id: 165012352
    {'aut_label': '2F', 'centralizer': '8.K', 'counter': 8, 'group_counter': 655, 'group_order': 6144, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 51212588579793007921, 'size': 8}
  • id: 165012363
    {'aut_label': '2H', 'centralizer': '12.CH', 'counter': 9, 'group_counter': 655, 'group_order': 6144, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 5606234750137, 'size': 12}
  • id: 165012276
    {'aut_label': '2H', 'centralizer': '12.CH', 'counter': 10, 'group_counter': 655, 'group_order': 6144, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 5606234755062, 'size': 12}
  • id: 165012277
    {'aut_label': '2H', 'centralizer': '12.CH', 'counter': 11, 'group_counter': 655, 'group_order': 6144, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 25903229687450757758137, 'size': 12}
  • id: 165012278
    {'aut_label': '2H', 'centralizer': '12.CH', 'counter': 12, 'group_counter': 655, 'group_order': 6144, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 25903229687450757763062, 'size': 12}
  • id: 165012279
    {'aut_label': '2L', 'centralizer': '24.G', 'counter': 13, 'group_counter': 655, 'group_order': 6144, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 372506484252216, 'size': 24}
  • id: 165012280
    {'aut_label': '2L', 'centralizer': '24.G', 'counter': 14, 'group_counter': 655, 'group_order': 6144, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 375302503331158, 'size': 24}
  • id: 165012281
    {'aut_label': '2N', 'centralizer': '24.CS', 'counter': 15, 'group_counter': 655, 'group_order': 6144, 'label': '2N', 'order': 2, 'powers': [1, 15], 'representative': 51091300648970236816, 'size': 24}
  • id: 165012282
    {'aut_label': '2N', 'centralizer': '24.CS', 'counter': 16, 'group_counter': 655, 'group_order': 6144, 'label': '2O', 'order': 2, 'powers': [1, 16], 'representative': 51091300648970241983, 'size': 24}
  • id: 165012283
    {'aut_label': '2P', 'centralizer': '24.GD', 'counter': 17, 'group_counter': 655, 'group_order': 6144, 'label': '2P', 'order': 2, 'powers': [1, 17], 'representative': 51091303471599674863, 'size': 24}
  • id: 165012284
    {'aut_label': '2L', 'centralizer': '24.G', 'counter': 18, 'group_counter': 655, 'group_order': 6144, 'label': '2Q', 'order': 2, 'powers': [1, 18], 'representative': 51212954172407328006, 'size': 24}
  • id: 165012285
    {'aut_label': '2L', 'centralizer': '24.G', 'counter': 19, 'group_counter': 655, 'group_order': 6144, 'label': '2R', 'order': 2, 'powers': [1, 19], 'representative': 51212956968427137863, 'size': 24}
  • id: 165012287
    {'aut_label': '2S', 'centralizer': '24.GU', 'counter': 20, 'group_counter': 655, 'group_order': 6144, 'label': '2S', 'order': 2, 'powers': [1, 20], 'representative': 53952291033885859905358, 'size': 24}
  • id: 165012288
    {'aut_label': '2T', 'centralizer': '24.GD', 'counter': 21, 'group_counter': 655, 'group_order': 6144, 'label': '2T', 'order': 2, 'powers': [1, 21], 'representative': 108169256548149195531001, 'size': 24}
  • id: 165012289
    {'aut_label': '2U', 'centralizer': '24.GU', 'counter': 22, 'group_counter': 655, 'group_order': 6144, 'label': '2U', 'order': 2, 'powers': [1, 22], 'representative': 53952413037457261852783, 'size': 24}
  • id: 165012290
    {'aut_label': '2V', 'centralizer': '32.F', 'counter': 23, 'group_counter': 655, 'group_order': 6144, 'label': '2V', 'order': 2, 'powers': [1, 23], 'representative': 25852272835140967219336, 'size': 32}
  • id: 165012291
    {'aut_label': '2V', 'centralizer': '32.F', 'counter': 24, 'group_counter': 655, 'group_order': 6144, 'label': '2W', 'order': 2, 'powers': [1, 24], 'representative': 25852272835140967224263, 'size': 32}
  • id: 165012292
    {'aut_label': '2X', 'centralizer': None, 'counter': 25, 'group_counter': 655, 'group_order': 6144, 'label': '2X', 'order': 2, 'powers': [1, 25], 'representative': 366906476160120, 'size': 48}
  • id: 165012293
    {'aut_label': '2Y', 'centralizer': None, 'counter': 26, 'group_counter': 655, 'group_order': 6144, 'label': '2Y', 'order': 2, 'powers': [1, 26], 'representative': 256106167404192137, 'size': 48}
  • id: 165012294
    {'aut_label': '2X', 'centralizer': None, 'counter': 27, 'group_counter': 655, 'group_order': 6144, 'label': '2Z', 'order': 2, 'powers': [1, 27], 'representative': 51212959784869466857, 'size': 48}
  • id: 165012295
    {'aut_label': '2Y', 'centralizer': None, 'counter': 28, 'group_counter': 655, 'group_order': 6144, 'label': '2AA', 'order': 2, 'powers': [1, 28], 'representative': 25903363787224050718222, 'size': 48}
  • id: 165012296
    {'aut_label': '3A', 'centralizer': None, 'counter': 29, 'group_counter': 655, 'group_order': 6144, 'label': '3A', 'order': 3, 'powers': [29, 1], 'representative': 350207540235483479942407, 'size': 128}
  • id: 165012298
    {'aut_label': '4A', 'centralizer': '6.K', 'counter': 30, 'group_counter': 655, 'group_order': 6144, 'label': '4A', 'order': 4, 'powers': [4, 30], 'representative': 2796059363782, 'size': 6}
  • id: 165012299
    {'aut_label': '4B', 'centralizer': '6.I', 'counter': 31, 'group_counter': 655, 'group_order': 6144, 'label': '4B', 'order': 4, 'powers': [4, 31], 'representative': 25903229684640582366857, 'size': 6}
  • id: 165012300
    {'aut_label': '4C', 'centralizer': '6.K', 'counter': 32, 'group_counter': 655, 'group_order': 6144, 'label': '4C', 'order': 4, 'powers': [4, 32], 'representative': 25903229684640582371782, 'size': 6}
  • id: 165012301
    {'aut_label': '4D', 'centralizer': '6.I', 'counter': 33, 'group_counter': 655, 'group_order': 6144, 'label': '4D', 'order': 4, 'powers': [4, 33], 'representative': 2796059358857, 'size': 6}
  • id: 165012302
    {'aut_label': '4E', 'centralizer': '8.Q', 'counter': 34, 'group_counter': 655, 'group_order': 6144, 'label': '4E', 'order': 4, 'powers': [5, 34], 'representative': 79804051672210232750640, 'size': 8}
  • id: 165012303
    {'aut_label': '4E', 'centralizer': '8.Q', 'counter': 35, 'group_counter': 655, 'group_order': 6144, 'label': '4F', 'order': 4, 'powers': [5, 35], 'representative': 79804173675793954832057, 'size': 8}
  • id: 165012304
    {'aut_label': '4G', 'centralizer': '12.Z', 'counter': 36, 'group_counter': 655, 'group_order': 6144, 'label': '4G', 'order': 4, 'powers': [4, 36], 'representative': 122003583856737857, 'size': 12}
  • id: 165012305
    {'aut_label': '4H', 'centralizer': '12.Z', 'counter': 37, 'group_counter': 655, 'group_order': 6144, 'label': '4H', 'order': 4, 'powers': [4, 37], 'representative': 122003583856732942, 'size': 12}
  • id: 165012306
    {'aut_label': '4I', 'centralizer': '24.H', 'counter': 38, 'group_counter': 655, 'group_order': 6144, 'label': '4I', 'order': 4, 'powers': [4, 38], 'representative': 372506484257143, 'size': 24}
  • id: 165012307
    {'aut_label': '4I', 'centralizer': '24.H', 'counter': 39, 'group_counter': 655, 'group_order': 6144, 'label': '4J', 'order': 4, 'powers': [4, 39], 'representative': 375302503336313, 'size': 24}
  • id: 165012309
    {'aut_label': '4K', 'centralizer': '24.FT', 'counter': 40, 'group_counter': 655, 'group_order': 6144, 'label': '4K', 'order': 4, 'powers': [4, 40], 'representative': 122006394111957822, 'size': 24}
  • id: 165012310
    {'aut_label': '4K', 'centralizer': '24.FT', 'counter': 41, 'group_counter': 655, 'group_order': 6144, 'label': '4L', 'order': 4, 'powers': [4, 41], 'representative': 122006394111962737, 'size': 24}
  • id: 165012311
    {'aut_label': '4M', 'centralizer': '24.ER', 'counter': 42, 'group_counter': 655, 'group_order': 6144, 'label': '4M', 'order': 4, 'powers': [5, 42], 'representative': 256450635744675257, 'size': 24}
  • id: 165012312
    {'aut_label': '4M', 'centralizer': '24.ER', 'counter': 43, 'group_counter': 655, 'group_order': 6144, 'label': '4N', 'order': 4, 'powers': [5, 43], 'representative': 256451949685617977, 'size': 24}
  • id: 165012313
    {'aut_label': '4O', 'centralizer': '24.FV', 'counter': 44, 'group_counter': 655, 'group_order': 6144, 'label': '4O', 'order': 4, 'powers': [4, 44], 'representative': 51091306255204986953, 'size': 24}
  • id: 165012314
    {'aut_label': '4P', 'centralizer': '24.FV', 'counter': 45, 'group_counter': 655, 'group_order': 6144, 'label': '4P', 'order': 4, 'powers': [4, 45], 'representative': 51091306255204991878, 'size': 24}
  • id: 165012315
    {'aut_label': '4I', 'centralizer': '24.H', 'counter': 46, 'group_counter': 655, 'group_order': 6144, 'label': '4Q', 'order': 4, 'powers': [4, 46], 'representative': 51212954172407333161, 'size': 24}
  • id: 165012316
    {'aut_label': '4I', 'centralizer': '24.H', 'counter': 47, 'group_counter': 655, 'group_order': 6144, 'label': '4R', 'order': 4, 'powers': [4, 47], 'representative': 51212956968427132936, 'size': 24}
  • id: 165012317
    {'aut_label': '4S', 'centralizer': '24.GN', 'counter': 48, 'group_counter': 655, 'group_order': 6144, 'label': '4S', 'order': 4, 'powers': [4, 48], 'representative': 53952291036669465199303, 'size': 24}
  • id: 165012318
    {'aut_label': '4T', 'centralizer': '24.GN', 'counter': 49, 'group_counter': 655, 'group_order': 6144, 'label': '4T', 'order': 4, 'powers': [4, 49], 'representative': 79855398716243993337478, 'size': 24}
  • id: 165012320
    {'aut_label': '4U', 'centralizer': None, 'counter': 50, 'group_counter': 655, 'group_order': 6144, 'label': '4U', 'order': 4, 'powers': [4, 50], 'representative': 366906476165047, 'size': 48}
  • id: 165012321
    {'aut_label': '4V', 'centralizer': None, 'counter': 51, 'group_counter': 655, 'group_order': 6144, 'label': '4V', 'order': 4, 'powers': [4, 51], 'representative': 256106167404197062, 'size': 48}
  • id: 165012322
    {'aut_label': '4U', 'centralizer': None, 'counter': 52, 'group_counter': 655, 'group_order': 6144, 'label': '4W', 'order': 4, 'powers': [4, 52], 'representative': 51212959784869461702, 'size': 48}
  • id: 165012323
    {'aut_label': '4V', 'centralizer': None, 'counter': 53, 'group_counter': 655, 'group_order': 6144, 'label': '4X', 'order': 4, 'powers': [4, 53], 'representative': 25903363787224050723137, 'size': 48}
  • id: 165012324
    {'aut_label': '4Y', 'centralizer': None, 'counter': 54, 'group_counter': 655, 'group_order': 6144, 'label': '4Y', 'order': 4, 'powers': [4, 54], 'representative': 54003382331738770057559, 'size': 48}
  • id: 165012325
    {'aut_label': '4Y', 'centralizer': None, 'counter': 55, 'group_counter': 655, 'group_order': 6144, 'label': '4Z', 'order': 4, 'powers': [4, 55], 'representative': 54003382331738770062712, 'size': 48}
  • id: 165012326
    {'aut_label': '4AA', 'centralizer': None, 'counter': 56, 'group_counter': 655, 'group_order': 6144, 'label': '4AA', 'order': 4, 'powers': [21, 56], 'representative': 378307935800261845482817, 'size': 96}
  • id: 165012327
    {'aut_label': '4AB', 'centralizer': None, 'counter': 57, 'group_counter': 655, 'group_order': 6144, 'label': '4AB', 'order': 4, 'powers': [5, 57], 'representative': 512278889087358536750646, 'size': 96}
  • id: 165012328
    {'aut_label': '4AC', 'centralizer': None, 'counter': 58, 'group_counter': 655, 'group_order': 6144, 'label': '4AC', 'order': 4, 'powers': [21, 58], 'representative': 324355523478471733634623, 'size': 96}
  • id: 165012329
    {'aut_label': '4AC', 'centralizer': None, 'counter': 59, 'group_counter': 655, 'group_order': 6144, 'label': '4AD', 'order': 4, 'powers': [21, 59], 'representative': 296041787654274544009672, 'size': 96}
  • id: 165012331
    {'aut_label': '4AA', 'centralizer': None, 'counter': 60, 'group_counter': 655, 'group_order': 6144, 'label': '4AE', 'order': 4, 'powers': [21, 60], 'representative': 162070577929270450575953, 'size': 96}
  • id: 165012332
    {'aut_label': '4AA', 'centralizer': None, 'counter': 61, 'group_counter': 655, 'group_order': 6144, 'label': '4AF', 'order': 4, 'powers': [21, 61], 'representative': 296092756952834189673463, 'size': 96}
  • id: 165012333
    {'aut_label': '4AA', 'centralizer': None, 'counter': 62, 'group_counter': 655, 'group_order': 6144, 'label': '4AG', 'order': 4, 'powers': [21, 62], 'representative': 486478219748194748793479, 'size': 96}
  • id: 165012334
    {'aut_label': '4AC', 'centralizer': None, 'counter': 63, 'group_counter': 655, 'group_order': 6144, 'label': '4AH', 'order': 4, 'powers': [21, 63], 'representative': 187922595023836588379392, 'size': 96}
  • id: 165012335
    {'aut_label': '4AB', 'centralizer': None, 'counter': 64, 'group_counter': 655, 'group_order': 6144, 'label': '4AI', 'order': 4, 'powers': [5, 64], 'representative': 270189392815529337790222, 'size': 96}
  • id: 165012336
    {'aut_label': '4AC', 'centralizer': None, 'counter': 65, 'group_counter': 655, 'group_order': 6144, 'label': '4AJ', 'order': 4, 'powers': [21, 65], 'representative': 187922595022535181311872, 'size': 96}
  • id: 165012337
    {'aut_label': '4AK', 'centralizer': None, 'counter': 66, 'group_counter': 655, 'group_order': 6144, 'label': '4AK', 'order': 4, 'powers': [22, 66], 'representative': 187922217286583882755192, 'size': 192}
  • id: 165012338
    {'aut_label': '4AK', 'centralizer': None, 'counter': 67, 'group_counter': 655, 'group_order': 6144, 'label': '4AL', 'order': 4, 'powers': [22, 67], 'representative': 620397054337642327077127, 'size': 192}
  • id: 165012339
    {'aut_label': '6A', 'centralizer': None, 'counter': 68, 'group_counter': 655, 'group_order': 6144, 'label': '6A', 'order': 6, 'powers': [29, 5], 'representative': 458377945446285832245822, 'size': 128}
  • id: 165012340
    {'aut_label': '6B', 'centralizer': None, 'counter': 69, 'group_counter': 655, 'group_order': 6144, 'label': '6B', 'order': 6, 'powers': [29, 2], 'representative': 512279023891384618428222, 'size': 128}
  • id: 165012342
    {'aut_label': '6C', 'centralizer': None, 'counter': 70, 'group_counter': 655, 'group_order': 6144, 'label': '6C', 'order': 6, 'powers': [29, 6], 'representative': 594596384623350519753742, 'size': 128}
  • id: 165012343
    {'aut_label': '6D', 'centralizer': None, 'counter': 71, 'group_counter': 655, 'group_order': 6144, 'label': '6D', 'order': 6, 'powers': [29, 7], 'representative': 242089374989297116488257, 'size': 256}
  • id: 165012344
    {'aut_label': '6E', 'centralizer': None, 'counter': 72, 'group_counter': 655, 'group_order': 6144, 'label': '6E', 'order': 6, 'powers': [29, 23], 'representative': 242089630728557830053240, 'size': 256}
  • id: 165012345
    {'aut_label': '6D', 'centralizer': None, 'counter': 73, 'group_counter': 655, 'group_order': 6144, 'label': '6F', 'order': 6, 'powers': [29, 8], 'representative': 540643972306971815251326, 'size': 256}
  • id: 165012346
    {'aut_label': '6E', 'centralizer': None, 'counter': 74, 'group_counter': 655, 'group_order': 6144, 'label': '6G', 'order': 6, 'powers': [29, 24], 'representative': 242089752725248374737297, 'size': 256}
  • id: 165012347
    {'aut_label': '8A', 'centralizer': None, 'counter': 75, 'group_counter': 655, 'group_order': 6144, 'label': '8A', 'order': 8, 'powers': [33, 75], 'representative': 256111767372004553, 'size': 48}
  • id: 165012348
    {'aut_label': '8A', 'centralizer': None, 'counter': 76, 'group_counter': 655, 'group_order': 6144, 'label': '8B', 'order': 8, 'powers': [33, 76], 'representative': 256111767372009478, 'size': 48}
  • id: 165012349
    {'aut_label': '8C', 'centralizer': None, 'counter': 77, 'group_counter': 655, 'group_order': 6144, 'label': '8C', 'order': 8, 'powers': [37, 77], 'representative': 256456241979420232, 'size': 48}
  • id: 165012350
    {'aut_label': '8C', 'centralizer': None, 'counter': 78, 'group_counter': 655, 'group_order': 6144, 'label': '8D', 'order': 8, 'powers': [37, 78], 'representative': 256456241979425159, 'size': 48}
  • id: 165012351
    {'aut_label': '8A', 'centralizer': None, 'counter': 79, 'group_counter': 655, 'group_order': 6144, 'label': '8E', 'order': 8, 'powers': [33, 79], 'representative': 25903363792824098364238, 'size': 48}
  • id: 165012353
    {'aut_label': '8A', 'centralizer': None, 'counter': 80, 'group_counter': 655, 'group_order': 6144, 'label': '8F', 'order': 8, 'powers': [33, 80], 'representative': 25903363792824098369153, 'size': 48}
  • id: 165012354
    {'aut_label': '8C', 'centralizer': None, 'counter': 81, 'group_counter': 655, 'group_order': 6144, 'label': '8G', 'order': 8, 'powers': [37, 81], 'representative': 25903364137298705054159, 'size': 48}
  • id: 165012355
    {'aut_label': '8C', 'centralizer': None, 'counter': 82, 'group_counter': 655, 'group_order': 6144, 'label': '8H', 'order': 8, 'powers': [37, 82], 'representative': 25903364137298705059072, 'size': 48}
  • id: 165012356
    {'aut_label': '8I', 'centralizer': None, 'counter': 83, 'group_counter': 655, 'group_order': 6144, 'label': '8I', 'order': 8, 'powers': [37, 83], 'representative': 53952291395173686827663, 'size': 48}
  • id: 165012357
    {'aut_label': '8I', 'centralizer': None, 'counter': 84, 'group_counter': 655, 'group_order': 6144, 'label': '8J', 'order': 8, 'powers': [37, 84], 'representative': 53952291395173686832576, 'size': 48}
  • id: 165012358
    {'aut_label': '8I', 'centralizer': None, 'counter': 85, 'group_counter': 655, 'group_order': 6144, 'label': '8K', 'order': 8, 'powers': [37, 85], 'representative': 53952291397969706609281, 'size': 48}
  • id: 165012359
    {'aut_label': '8I', 'centralizer': None, 'counter': 86, 'group_counter': 655, 'group_order': 6144, 'label': '8L', 'order': 8, 'powers': [37, 86], 'representative': 53952291397969706614446, 'size': 48}
  • id: 165012360
    {'aut_label': '8M', 'centralizer': None, 'counter': 87, 'group_counter': 655, 'group_order': 6144, 'label': '8M', 'order': 8, 'powers': [33, 87], 'representative': 187973429511254312217743, 'size': 96}
  • id: 165012361
    {'aut_label': '8N', 'centralizer': None, 'counter': 88, 'group_counter': 655, 'group_order': 6144, 'label': '8N', 'order': 8, 'powers': [37, 88], 'representative': 216237735977946422313726, 'size': 96}
  • id: 165012362
    {'aut_label': '8O', 'centralizer': None, 'counter': 89, 'group_counter': 655, 'group_order': 6144, 'label': '8O', 'order': 8, 'powers': [37, 89], 'representative': 324355523486867760758417, 'size': 96}
  • id: 165012364
    {'aut_label': '8O', 'centralizer': None, 'counter': 90, 'group_counter': 655, 'group_order': 6144, 'label': '8P', 'order': 8, 'powers': [37, 90], 'representative': 458326854512510541436822, 'size': 96}
  • id: 165012365
    {'aut_label': '8N', 'centralizer': None, 'counter': 91, 'group_counter': 655, 'group_order': 6144, 'label': '8Q', 'order': 8, 'powers': [37, 91], 'representative': 512329980388007332051337, 'size': 96}
  • id: 165012366
    {'aut_label': '8M', 'centralizer': None, 'counter': 92, 'group_counter': 655, 'group_order': 6144, 'label': '8R', 'order': 8, 'powers': [33, 92], 'representative': 134021650664481560052359, 'size': 96}
  • id: 165012367
    {'aut_label': '8S', 'centralizer': None, 'counter': 93, 'group_counter': 655, 'group_order': 6144, 'label': '8S', 'order': 8, 'powers': [49, 93], 'representative': 162121291492687272316921, 'size': 192}
  • id: 165012368
    {'aut_label': '8S', 'centralizer': None, 'counter': 94, 'group_counter': 655, 'group_order': 6144, 'label': '8T', 'order': 8, 'powers': [49, 94], 'representative': 187973307868964644494696, 'size': 192}
  • id: 165012369
    {'aut_label': '12A', 'centralizer': None, 'counter': 95, 'group_counter': 655, 'group_order': 6144, 'label': '12A', 'order': 12, 'powers': [68, 34], 'representative': 378307558429923759408127, 'size': 256}
  • id: 165012370
    {'aut_label': '12A', 'centralizer': None, 'counter': 96, 'group_counter': 655, 'group_order': 6144, 'label': '12B', 'order': 12, 'powers': [68, 35], 'representative': 296092500869098694505479, 'size': 256}
• 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: 16521875
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16521886
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 16521897
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 16521908
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 16521919
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 16521930
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 16521941
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 16521952
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 16521963
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 16521876
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16521877
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16521878
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16521879
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16521880
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16521881
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16521882
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16521883
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, -1, -1], 'schur_index': 1}
  • id: 16521884
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, 0, 0, -2, 2, 0, -2, -2, 2, -2, -2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 2, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521885
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, 0, 0, -2, 2, 0, 2, 2, -2, -2, -2, 2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, -2, -2, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521887
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, -2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 2, 2, 0, 2, -2, 2, 2, -2, -2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 2, -2, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521888
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 2, 2, 0, -2, 2, -2, 2, -2, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, -2, 2, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521889
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 0, -2, 2, -2, 0, 0, -2, 2, 0, -2, 2, 0, 0, 0, 0, -1, 2, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, -2, 2, -2, 2, 2, 0, -2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, -1, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 1, -1], 'schur_index': 1}
  • id: 16521890
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 0, -2, 2, -2, 0, 0, -2, 2, 0, 2, -2, 0, 0, 0, 0, -1, 2, 2, -2, -2, 2, -2, -2, 2, 2, 0, 0, 0, -2, 2, -2, 2, -2, 0, -2, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, -1, 1, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, -1, 1], 'schur_index': 1}
  • id: 16521891
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 2, -2, 2, 0, 2, -2, -2, 0, 0, -2, 2, 0, -2, 2, 0, 0, 0, 0, -1, 2, 2, -2, -2, 2, -2, -2, 2, -2, 0, 0, 0, -2, 2, -2, 2, -2, 0, 2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1, 1, -1, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, -1, 1], 'schur_index': 1}
  • id: 16521892
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 2, -2, 2, 0, 2, -2, -2, 0, 0, -2, 2, 0, 2, -2, 0, 0, 0, 0, -1, 2, 2, -2, -2, -2, 2, -2, 2, -2, 0, 0, 0, -2, 2, -2, 2, 2, 0, 2, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1, -1, 1, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, 1, -1], 'schur_index': 1}
  • id: 16521893
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 0, -2, -2, 2, 0, 0, 2, 2, 0, -2, -2, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 0, -2, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 2, 0, 0, -1, -1], 'schur_index': 1}
  • id: 16521894
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 0, -2, -2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, -1, 2, 2, 2, 2, -2, -2, 2, 2, -2, 0, 0, 0, 2, 2, 2, 2, -2, 0, -2, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1, -1, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, -2, 0, 0, 1, 1], 'schur_index': 1}
  • id: 16521895
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, -2, -2, 0, 0, 0, 0, -1, 2, 2, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, -2, 0, 2, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, 1, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 1, 1], 'schur_index': 1}
  • id: 16521896
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, 1, 3, 3, -1, 1, 1, -1, -1, 1, 3, 3, 1, 1, 1, 1, 0, 3, 3, 3, 3, 3, 3, 3, 3, -1, 1, 1, 1, -1, -1, -1, -1, 3, 1, -1, 3, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16521898
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, 0, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, 3, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16521899
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 3, -3, -3, 3, 1, -1, 1, -1, -1, -1, -3, 3, 1, 1, 1, 1, -1, -1, -3, 3, -1, -1, 1, 1, 0, 3, 3, -3, -3, -3, 3, -3, 3, -1, 1, -1, -1, 1, -1, 1, -1, 3, 1, 1, -3, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 0, 0], 'schur_index': 1}
  • id: 16521900
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 3, -3, -3, 3, 1, -1, 1, -1, -1, -1, -3, 3, 1, 1, 1, 1, -1, -1, 3, -3, 1, -1, 1, -1, 0, 3, 3, -3, -3, 3, -3, -3, 3, -1, 1, -1, -1, 1, -1, 1, -1, -3, 1, 1, 3, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 0, 0], 'schur_index': 1}
  • id: 16521901
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 3, -3, -3, 3, 1, -1, 1, -1, -1, 1, -3, 3, 1, -1, -1, 1, -1, 1, -3, 3, 1, 1, -1, -1, 0, 3, 3, -3, -3, -3, 3, -3, 3, -1, -1, 1, 1, 1, -1, 1, -1, 3, -1, 1, -3, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 0, 0], 'schur_index': 1}
  • id: 16521902
    {'cdim': 3, 'counter': 34, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 3, -3, -3, 3, 1, -1, 1, -1, -1, 1, -3, 3, 1, -1, -1, 1, -1, 1, 3, -3, -1, 1, -1, 1, 0, 3, 3, -3, -3, 3, -3, -3, 3, -1, -1, 1, 1, 1, -1, 1, -1, -3, -1, 1, 3, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 0, 0], 'schur_index': 1}
  • id: 16521903
    {'cdim': 3, 'counter': 35, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 3, -3, 3, -3, -1, 1, -1, 1, -1, -1, 3, -3, 1, 1, 1, 1, -1, -1, -3, 3, -1, 1, -1, 1, 0, 3, 3, -3, -3, 3, -3, -3, 3, 1, 1, -1, -1, 1, -1, 1, -1, -3, 1, -1, 3, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 0, 0], 'schur_index': 1}
  • id: 16521904
    {'cdim': 3, 'counter': 36, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 3, -3, 3, -3, -1, 1, -1, 1, -1, -1, 3, -3, 1, 1, 1, 1, -1, -1, 3, -3, 1, 1, -1, -1, 0, 3, 3, -3, -3, -3, 3, -3, 3, 1, 1, -1, -1, 1, -1, 1, -1, 3, 1, -1, -3, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 0, 0], 'schur_index': 1}
  • id: 16521905
    {'cdim': 3, 'counter': 37, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3i', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 3, -3, 3, -3, -1, 1, -1, 1, -1, 1, 3, -3, 1, -1, -1, 1, -1, 1, -3, 3, 1, -1, 1, -1, 0, 3, 3, -3, -3, 3, -3, -3, 3, 1, -1, 1, 1, 1, -1, 1, -1, -3, -1, -1, 3, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 0, 0], 'schur_index': 1}
  • id: 16521906
    {'cdim': 3, 'counter': 38, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3j', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 3, -3, 3, -3, -1, 1, -1, 1, -1, 1, 3, -3, 1, -1, -1, 1, -1, 1, 3, -3, -1, -1, 1, 1, 0, 3, 3, -3, -3, -3, 3, -3, 3, 1, -1, 1, 1, 1, -1, 1, -1, 3, -1, -1, -3, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 0, 0], 'schur_index': 1}
  • id: 16521907
    {'cdim': 3, 'counter': 39, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3k', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -3, -3, 1, 1, 1, 1, -1, -1, -3, -3, -1, -1, -1, -1, -1, -1, -3, -3, 1, 1, 1, 1, 0, 3, 3, 3, 3, 3, 3, 3, 3, 1, -1, -1, -1, -1, -1, -1, -1, 3, -1, 1, 3, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16521909
    {'cdim': 3, 'counter': 40, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3l', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -3, -3, 1, 1, 1, 1, -1, -1, -3, -3, -1, -1, -1, -1, -1, -1, 3, 3, -1, 1, 1, -1, 0, 3, 3, 3, 3, -3, -3, 3, 3, 1, -1, -1, -1, -1, -1, -1, -1, -3, -1, 1, -3, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16521910
    {'cdim': 3, 'counter': 41, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3m', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -3, -3, 1, 1, 1, 1, -1, 1, -3, -3, -1, 1, 1, -1, -1, 1, -3, -3, -1, -1, -1, -1, 0, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, -1, -1, -1, -1, 3, 1, 1, 3, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16521911
    {'cdim': 3, 'counter': 42, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3n', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, -3, -3, 1, 1, 1, 1, -1, 1, -3, -3, -1, 1, 1, -1, -1, 1, 3, 3, 1, -1, -1, 1, 0, 3, 3, 3, 3, -3, -3, 3, 3, 1, 1, 1, 1, -1, -1, -1, -1, -3, 1, 1, -3, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16521912
    {'cdim': 3, 'counter': 43, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3o', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -3, -3, 1, -1, -1, 1, 0, 3, 3, 3, 3, -3, -3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -3, -1, -1, -3, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 16521913
    {'cdim': 3, 'counter': 44, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.3p', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, 1, 3, 3, -1, 1, 1, -1, -1, 1, -3, -3, -1, 1, 1, -1, 0, 3, 3, 3, 3, -3, -3, 3, 3, -1, 1, 1, 1, -1, -1, -1, -1, -3, 1, -1, -3, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 16521914
    {'cdim': 4, 'counter': 45, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -4, -4, 4, 4, 0, 0, -4, 4, 0, 0, 0, 0, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521915
    {'cdim': 4, 'counter': 46, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.4b', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -4, -4, -4, -4, 0, 0, 4, 4, 0, 0, 0, 0, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521916
    {'cdim': 6, 'counter': 47, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6a', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, -2, -2, -2, -2, -2, 0, -2, -2, 2, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 2, 0, -2, -2, -2, -2, 0, 0, -2, -2, -2, 0, 0, 0, 2, -2, -2, 2, 0, 0, -2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521917
    {'cdim': 6, 'counter': 48, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6b', 'multiplicity': 1, 'nt': [8, 41], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 0, 0, 0, 2, 2, 0, 0, -2, -2, -2, -2, 0, 0, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, 0, 2, 2, 0, -2, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521918
    {'cdim': 6, 'counter': 49, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6c', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -6, 6, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, 0, 0, -6, 6, 0, -2, -2, 2, 2, 2, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521920
    {'cdim': 6, 'counter': 50, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6d', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -6, 6, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, 0, 0, -6, 6, 0, 2, 2, -2, 2, 2, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521921
    {'cdim': 6, 'counter': 51, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6e', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, 6, 6, 0, 2, -2, 2, -2, 2, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521922
    {'cdim': 6, 'counter': 52, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6f', 'multiplicity': 1, 'nt': [12, 86], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, 6, 6, 0, -2, 2, -2, -2, 2, 2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521923
    {'cdim': 6, 'counter': 53, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6g', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, -2, -2, -2, -2, -2, 0, -2, -2, 2, 0, 0, -2, 2, 0, 0, 0, -2, 0, 0, -2, 0, -2, -2, -2, -2, 0, 0, -2, -2, -2, 0, 0, 0, 2, -2, -2, 2, 0, 0, -2, 0, 2, -2, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521924
    {'cdim': 6, 'counter': 54, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6h', 'multiplicity': 1, 'nt': [12, 108], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 0, 0, 0, -2, -2, 0, 0, -2, -2, -2, -2, 0, 0, -2, -2, 2, -2, -2, -2, -2, 2, 2, -2, 0, -2, 2, 0, -2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521925
    {'cdim': 6, 'counter': 55, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6i', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, -6, -6, 6, -2, 2, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, -2, 2, 0, 0, -2, -2, 2, 2, 0, 0, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 0, 2, -2, 0, -2, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521926
    {'cdim': 6, 'counter': 56, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6j', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, -6, -6, 6, -2, 2, -2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 2, -2, 0, 0, -2, -2, 2, 2, 0, 0, 2, -2, 2, -2, 2, 2, 2, 2, -2, -2, 0, -2, -2, 0, -2, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, -2, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521927
    {'cdim': 6, 'counter': 57, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6k', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, -6, -6, 6, 2, -2, 2, -2, -2, 0, 2, -2, -2, 0, 0, 2, 2, 0, 0, 0, -2, 0, 0, 2, 0, -2, -2, 2, 2, 0, 0, 2, -2, -2, 0, 0, 0, -2, -2, 2, 2, 0, 0, 2, 0, 2, 2, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521928
    {'cdim': 6, 'counter': 58, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6l', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, -6, -6, 6, 2, -2, 2, -2, -2, 0, 2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, -2, 0, -2, -2, 2, 2, 0, 0, 2, -2, -2, 0, 0, 0, -2, -2, 2, 2, 0, 0, 2, 0, 2, -2, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521929
    {'cdim': 6, 'counter': 59, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6m', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, -6, 6, -6, -2, 2, -2, 2, -2, 0, -2, 2, -2, 0, 0, 2, 2, 0, 0, 0, -2, 0, 0, 2, 0, -2, -2, 2, 2, 0, 0, 2, -2, 2, 0, 0, 0, -2, -2, 2, 2, 0, 0, -2, 0, -2, 2, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521931
    {'cdim': 6, 'counter': 60, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6n', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, -6, 6, -6, -2, 2, -2, 2, -2, 0, -2, 2, -2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, -2, 0, -2, -2, 2, 2, 0, 0, 2, -2, 2, 0, 0, 0, -2, -2, 2, 2, 0, 0, -2, 0, -2, -2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521932
    {'cdim': 6, 'counter': 61, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6o', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, -6, 6, -6, 2, -2, 2, -2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 2, -2, 0, 0, -2, -2, 2, 2, 0, 0, 2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 0, 2, 2, 0, 2, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521933
    {'cdim': 6, 'counter': 62, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6p', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, -6, 6, -6, 2, -2, 2, -2, 2, 2, -2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, -2, 2, 0, 0, -2, -2, 2, 2, 0, 0, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 0, -2, 2, 0, 2, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, -2, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521934
    {'cdim': 6, 'counter': 63, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6q', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, -6, -6, -2, -2, -2, -2, 2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 0, 0, 0, 2, 2, 0, 0, -2, -2, -2, -2, 0, 0, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 0, -2, -2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521935
    {'cdim': 6, 'counter': 64, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6r', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, -6, -6, -2, -2, -2, -2, 2, 2, 2, 2, -2, 2, 2, 2, -2, 2, 0, 0, 0, -2, -2, 0, 0, -2, -2, -2, -2, 0, 0, -2, -2, -2, 2, 2, 2, -2, 2, 2, -2, 0, 2, -2, 0, 2, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521936
    {'cdim': 6, 'counter': 65, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6s', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, -6, -6, 2, 2, 2, 2, -2, 0, 2, 2, 2, 0, 0, -2, 2, 0, 0, 0, -2, 0, 0, -2, 0, -2, -2, -2, -2, 0, 0, -2, -2, 2, 0, 0, 0, 2, -2, -2, 2, 0, 0, 2, 0, -2, -2, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521937
    {'cdim': 6, 'counter': 66, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6t', 'multiplicity': 1, 'nt': [12, 136], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, -6, -6, 2, 2, 2, 2, -2, 0, 2, 2, 2, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 2, 0, -2, -2, -2, -2, 0, 0, -2, -2, 2, 0, 0, 0, 2, -2, -2, 2, 0, 0, 2, 0, -2, 2, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521938
    {'cdim': 6, 'counter': 67, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6u', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -6, 6, 0, 0, -4, 4, -4, 4, 2, -2, 0, 0, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 2, -2, -4, -2, -2, 2, 2, -2, 2, -2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521939
    {'cdim': 6, 'counter': 68, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6v', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -6, 6, 0, 0, -4, 4, -4, 4, 2, 2, 0, 0, -2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 2, -2, -4, 2, 2, -2, 2, -2, 2, -2, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521940
    {'cdim': 6, 'counter': 69, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6w', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -6, 6, 0, 0, 4, -4, 4, -4, 2, -2, 0, 0, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 2, -2, 4, -2, -2, 2, 2, -2, 2, -2, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521942
    {'cdim': 6, 'counter': 70, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6x', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -6, 6, 0, 0, 4, -4, 4, -4, 2, 2, 0, 0, -2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 2, -2, 4, 2, 2, -2, 2, -2, 2, -2, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521943
    {'cdim': 6, 'counter': 71, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6y', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 0, 0, -4, -4, -4, -4, 2, -2, 0, 0, 2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -2, -2, 4, 2, -2, 2, -2, -2, -2, -2, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521944
    {'cdim': 6, 'counter': 72, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6z', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 0, 0, -4, -4, -4, -4, 2, 2, 0, 0, 2, -2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -2, -2, 4, -2, 2, -2, -2, -2, -2, -2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521945
    {'cdim': 6, 'counter': 73, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6aa', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 0, 0, 4, 4, 4, 4, 2, -2, 0, 0, 2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -2, -2, -4, 2, -2, 2, -2, -2, -2, -2, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521946
    {'cdim': 6, 'counter': 74, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.6ab', 'multiplicity': 1, 'nt': [12, 186], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, 0, 0, 4, 4, 4, 4, 2, 2, 0, 0, 2, -2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -2, -2, -4, -2, 2, -2, -2, -2, -2, -2, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521947
    {'cdim': 12, 'counter': 75, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12a', 'multiplicity': 1, 'nt': [24, 1557], 'qdim': 12, 'qvalues': [12, -12, -12, 12, -12, 12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 0, 0, 4, -4, 0, 0, 0, 0, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521948
    {'cdim': 12, 'counter': 76, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12b', 'multiplicity': 1, 'nt': [24, 1557], 'qdim': 12, 'qvalues': [12, 12, 12, 12, -12, -12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, -4, -4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521949
    {'cdim': 12, 'counter': 77, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12c', 'multiplicity': 1, 'nt': [24, 7075], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, -4, -4, 4, 4, 0, -2, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 2, -2, -2, 2, 0, -4, 4, -4, 4, -6, -6, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 2, 2, 0, 2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 2, 2, -2, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521950
    {'cdim': 12, 'counter': 78, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12d', 'multiplicity': 1, 'nt': [24, 7075], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, 4, 4, -4, -4, 0, 2, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 2, -2, -2, 2, 0, -4, 4, -4, 4, -6, -6, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 2, -2, 0, 2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, -2, 2, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521951
    {'cdim': 12, 'counter': 79, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12e', 'multiplicity': 1, 'nt': [24, 7076], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, -4, -4, 4, 4, 0, 2, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, -2, 2, 2, -2, 0, -4, 4, -4, 4, -6, -6, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 2, -2, 0, 2, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, -2, 2, 2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521953
    {'cdim': 12, 'counter': 80, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12f', 'multiplicity': 1, 'nt': [24, 7076], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, 4, 4, -4, -4, 0, -2, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, -2, 2, 2, -2, 0, -4, 4, -4, 4, -6, -6, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 2, -2, -2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521954
    {'cdim': 12, 'counter': 81, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12g', 'multiplicity': 1, 'nt': [24, 7077], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, -4, -4, 4, 4, 0, -2, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, -2, -2, -2, -2, 0, -4, 4, -4, 4, 6, 6, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, -2, 2, 0, -2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, -2, 2, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521955
    {'cdim': 12, 'counter': 82, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12h', 'multiplicity': 1, 'nt': [24, 7077], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, 4, 4, -4, -4, 0, 2, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, -2, -2, -2, -2, 0, -4, 4, -4, 4, 6, 6, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, -2, -2, 0, -2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 2, 2, -2, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521956
    {'cdim': 12, 'counter': 83, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12i', 'multiplicity': 1, 'nt': [24, 7085], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, -4, -4, 4, 4, 0, 2, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 2, 2, 2, 2, 0, -4, 4, -4, 4, 6, 6, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, -2, -2, 0, -2, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 2, -2, -2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521957
    {'cdim': 12, 'counter': 84, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12j', 'multiplicity': 1, 'nt': [24, 7085], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, 4, 4, -4, -4, 0, -2, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, -4, 4, -4, 4, 6, 6, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, -2, 2, 0, -2, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, -2, 2, 2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521958
    {'cdim': 12, 'counter': 85, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12k', 'multiplicity': 1, 'nt': [24, 9107], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, -4, 4, 4, -4, 0, -2, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, -2, 2, -2, 2, 0, -4, 4, 4, -4, 6, -6, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 2, -2, 0, -2, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, -2, -2, 2, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521959
    {'cdim': 12, 'counter': 86, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12l', 'multiplicity': 1, 'nt': [24, 9107], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, -4, 4, 4, -4, 0, -2, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 2, 2, -2, -2, 0, -4, 4, 4, -4, -6, 6, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, -2, -2, 0, 2, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 2, -2, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521960
    {'cdim': 12, 'counter': 87, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12m', 'multiplicity': 1, 'nt': [24, 9107], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, -4, 4, 4, -4, 0, 2, 0, 0, 0, 2, -2, 0, 0, -2, 0, 0, -2, -2, 2, 2, 0, -4, 4, 4, -4, -6, 6, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, 2, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 2, 2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521961
    {'cdim': 12, 'counter': 88, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12n', 'multiplicity': 1, 'nt': [24, 9107], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, -4, 4, 4, -4, 0, 2, 0, 0, 0, 2, -2, 0, 0, -2, 0, 0, 2, -2, 2, -2, 0, -4, 4, 4, -4, 6, -6, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 2, 2, 0, -2, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, -2, -2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521962
    {'cdim': 12, 'counter': 89, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12o', 'multiplicity': 1, 'nt': [24, 9107], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, 4, -4, -4, 4, 0, -2, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, -2, -2, 2, 2, 0, -4, 4, 4, -4, -6, 6, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, -2, -2, 0, 2, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, -2, -2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521964
    {'cdim': 12, 'counter': 90, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12p', 'multiplicity': 1, 'nt': [24, 9107], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, 4, -4, -4, 4, 0, -2, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 2, -2, 2, -2, 0, -4, 4, 4, -4, 6, -6, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 2, -2, 0, -2, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 2, 2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521965
    {'cdim': 12, 'counter': 91, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12q', 'multiplicity': 1, 'nt': [24, 9107], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, 4, -4, -4, 4, 0, 2, 0, 0, 0, 2, -2, 0, 0, -2, 0, 0, -2, 2, -2, 2, 0, -4, 4, 4, -4, 6, -6, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 2, 2, 0, -2, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 2, -2, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521966
    {'cdim': 12, 'counter': 92, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.12r', 'multiplicity': 1, 'nt': [24, 9107], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, 4, -4, -4, 4, 0, 2, 0, 0, 0, 2, -2, 0, 0, -2, 0, 0, 2, 2, -2, -2, 0, -4, 4, 4, -4, -6, 6, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, 2, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, -2, -2, 2, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521967
    {'cdim': 24, 'counter': 93, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.24a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, -24, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, -8, -8, 8, 0, 0, 0, 0, 0, -4, 4, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521968
    {'cdim': 24, 'counter': 94, 'faithful': True, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.24b', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, -24, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, -8, -8, 8, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521969
    {'cdim': 24, 'counter': 95, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.24c', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, 24, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, -8, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16521970
    {'cdim': 24, 'counter': 96, 'faithful': False, 'group': '6144.ze', 'group_order': 6144, 'image': None, 'label': '6144.ze.24d', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, 24, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, -8, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 36715929
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 6144, 'label': '6144.ze.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 36715940
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 36715951
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[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: 36715962
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 36715973
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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: 36715984
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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: 36715995
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[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: 36716006
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 36716017
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 36715930
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 36715931
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 36715932
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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: 36715933
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[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: 36715934
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-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: 36715935
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 36715936
    {'center': None, 'center_index': 1, 'center_order': 6144, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 3072, 'label': '6144.ze.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 36715937
    {'center': None, 'center_index': 6, 'center_order': 1024, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': None, 'kernel_order': 1024, 'label': '6144.ze.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36715938
    {'center': None, 'center_index': 4, 'center_order': 1536, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 8, 'indicator': 1, 'kernel': None, 'kernel_order': 768, 'label': '6144.ze.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715939
    {'center': None, 'center_index': 4, 'center_order': 1536, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 8, 'indicator': 1, 'kernel': None, 'kernel_order': 768, 'label': '6144.ze.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715941
    {'center': None, 'center_index': 4, 'center_order': 1536, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 8, 'indicator': 1, 'kernel': None, 'kernel_order': 768, 'label': '6144.ze.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715942
    {'center': None, 'center_index': 4, 'center_order': 1536, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 8, 'indicator': 1, 'kernel': None, 'kernel_order': 768, 'label': '6144.ze.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715943
    {'center': None, 'center_index': 6, 'center_order': 1024, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 512, 'label': '6144.ze.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 36715944
    {'center': None, 'center_index': 6, 'center_order': 1024, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 512, 'label': '6144.ze.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 36715945
    {'center': None, 'center_index': 6, 'center_order': 1024, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 512, 'label': '6144.ze.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 36715946
    {'center': None, 'center_index': 6, 'center_order': 1024, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 512, 'label': '6144.ze.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 36715947
    {'center': None, 'center_index': 6, 'center_order': 1024, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 512, 'label': '6144.ze.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36715948
    {'center': None, 'center_index': 6, 'center_order': 1024, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 512, 'label': '6144.ze.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36715949
    {'center': None, 'center_index': 6, 'center_order': 1024, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': None, 'kernel_order': 512, 'label': '6144.ze.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36715950
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 29, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 256, 'label': '6144.ze.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715952
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 30, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 24, 'indicator': 1, 'kernel': None, 'kernel_order': 256, 'label': '6144.ze.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715953
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 31, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715954
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 32, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715955
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 33, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715956
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 34, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715957
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 35, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715958
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 36, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715959
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 37, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3i', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715960
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 38, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3j', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715961
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 39, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3k', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715963
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 40, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3l', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715964
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 41, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3m', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715965
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 42, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3n', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715966
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 43, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3o', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715967
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 44, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.3p', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715968
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715969
    {'center': None, 'center_index': 24, 'center_order': 256, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 48, 'indicator': 1, 'kernel': None, 'kernel_order': 128, 'label': '6144.ze.4b', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715970
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 47, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '6144.ze.6a', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715999
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 73, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.6aa', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716000
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 74, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.6ab', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715971
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 48, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '6144.ze.6b', 'nt': [8, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715972
    {'center': None, 'center_index': 96, 'center_order': 64, 'counter': 49, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '6144.ze.6c', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715974
    {'center': None, 'center_index': 96, 'center_order': 64, 'counter': 50, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '6144.ze.6d', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715975
    {'center': None, 'center_index': 96, 'center_order': 64, 'counter': 51, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '6144.ze.6e', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715976
    {'center': None, 'center_index': 96, 'center_order': 64, 'counter': 52, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '6144.ze.6f', 'nt': [12, 86], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715977
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 53, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '6144.ze.6g', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715978
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 54, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 192, 'indicator': 1, 'kernel': None, 'kernel_order': 32, 'label': '6144.ze.6h', 'nt': [12, 108], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715979
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 55, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6i', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715980
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 56, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6j', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715981
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 57, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6k', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715982
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 58, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6l', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715983
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 59, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6m', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715985
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 60, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6n', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715986
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 61, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6o', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715987
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 62, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6p', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715988
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 63, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6q', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715989
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 64, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6r', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715990
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 65, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6s', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715991
    {'center': None, 'center_index': 192, 'center_order': 32, 'counter': 66, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 384, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '6144.ze.6t', 'nt': [12, 136], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715992
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 67, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.6u', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715993
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 68, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.6v', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715994
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 69, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.6w', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715996
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 70, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.6x', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715997
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 71, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.6y', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36715998
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 72, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.6z', 'nt': [12, 186], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716001
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 75, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.12a', 'nt': [24, 1557], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716002
    {'center': None, 'center_index': 384, 'center_order': 16, 'counter': 76, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 768, 'indicator': 1, 'kernel': None, 'kernel_order': 8, 'label': '6144.ze.12b', 'nt': [24, 1557], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716003
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 77, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.12c', 'nt': [24, 7075], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716004
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 78, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.12d', 'nt': [24, 7075], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716005
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 79, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.12e', 'nt': [24, 7076], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716007
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 80, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.12f', 'nt': [24, 7076], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716008
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 81, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.12g', 'nt': [24, 7077], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716009
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 82, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.12h', 'nt': [24, 7077], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716010
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 83, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.12i', 'nt': [24, 7085], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716011
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 84, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.12j', 'nt': [24, 7085], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716012
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 85, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.12k', 'nt': [24, 9107], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716013
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 86, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.12l', 'nt': [24, 9107], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716014
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 87, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.12m', 'nt': [24, 9107], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716015
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 88, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.12n', 'nt': [24, 9107], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716016
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 89, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.12o', 'nt': [24, 9107], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716018
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 90, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.12p', 'nt': [24, 9107], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716019
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 91, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.12q', 'nt': [24, 9107], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716020
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 92, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.12r', 'nt': [24, 9107], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716021
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 93, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.24a', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716022
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 94, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': '6144.ze', 'image_order': 6144, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '6144.ze.24b', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716023
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 95, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.24c', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[24, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36716024
    {'center': None, 'center_index': 3072, 'center_order': 2, 'counter': 96, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '6144.ze', 'group_counter': 655, 'group_order': 6144, 'image': None, 'image_isoclass': None, 'image_order': 3072, 'indicator': 1, 'kernel': None, 'kernel_order': 2, 'label': '6144.ze.24d', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[24, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 229890644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 6144, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '6144.ze.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6144.ze', 'subgroup_hash': 4158378184127417885, 'subgroup_order': 6144, 'subgroup_tex': 'C_4^3:(C_2^2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3072, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.2.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': 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': '3072.sh', 'subgroup_hash': 4230291883527654367, 'subgroup_order': 3072, 'subgroup_tex': 'C_2^6:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3072, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3072.tl', 'subgroup_hash': 8234199900922918367, 'subgroup_order': 3072, 'subgroup_tex': 'C_4^3:(C_2^2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3072, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.2.C', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3072.vd', 'subgroup_hash': 3342409311411687120, 'subgroup_order': 3072, 'subgroup_tex': 'C_2\\times C_4^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3072, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.2.D', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3927960459847131087, 'subgroup_order': 3072, 'subgroup_tex': 'C_4^2:A_4.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 229891199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3072, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.2.E', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3072.yr', 'subgroup_hash': 7500238549280470531, 'subgroup_order': 3072, 'subgroup_tex': 'C_2\\times C_4^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3072, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.2.F', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3072.xn', 'subgroup_hash': 5231021295918148510, 'subgroup_order': 3072, 'subgroup_tex': 'C_2\\times C_4^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3072, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.2.G', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3072.zr', 'subgroup_hash': 4795080385471092725, 'subgroup_order': 3072, 'subgroup_tex': 'C_2\\times C_4^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3072, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '6144.ze.2.H', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3072.bgb', 'subgroup_hash': 7983714371117797868, 'subgroup_order': 3072, 'subgroup_tex': 'C_4^3:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1024, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '6144.ze.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8221984151569513336, 'subgroup_order': 2048, 'subgroup_tex': 'C_2^2.C_2^6.C_2^3', 'supersolvable': True, 'sylow': 2}
  • id: 229890656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1536, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408544218', 'subgroup_hash': 8839127453076449189, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^6:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1536, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408640177', 'subgroup_hash': 2071076170149121975, 'subgroup_order': 1536, 'subgroup_tex': '(C_2^2\\times C_4^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1536, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408531868', 'subgroup_hash': 4541057298709718937, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.(C_2^3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1536, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408640178', 'subgroup_hash': 8491451551449076452, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.(C_2^2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1536, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408640177', 'subgroup_hash': 2071076170149121975, 'subgroup_order': 1536, 'subgroup_tex': '(C_2^2\\times C_4^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1536, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408527290', 'subgroup_hash': 3052085908876179529, 'subgroup_order': 1536, 'subgroup_tex': 'C_2\\times C_4^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1536, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408633422', 'subgroup_hash': 6744575318357989330, 'subgroup_order': 1536, 'subgroup_tex': '(C_2^2\\times C_4^2).S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1536, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408640541', 'subgroup_hash': 8944755179417135467, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^5:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1536, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408527547', 'subgroup_hash': 3316927255007698598, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^3:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1536, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408633532', 'subgroup_hash': 7006179242975571382, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1536, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408550734', 'subgroup_hash': 7456160622201197021, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.(C_2^2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1536, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408544807', 'subgroup_hash': 8450812584686924886, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1536, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408545563', 'subgroup_hash': 6245505773554357918, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1536, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.4.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408544809', 'subgroup_hash': 631148683583985753, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.4.O', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1536.408610999', 'subgroup_hash': 7520617873431573928, 'subgroup_order': 1536, 'subgroup_tex': 'C_2\\times C_4^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229890822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.4.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1536.408640176', 'subgroup_hash': 897929048780159773, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.4.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1536.408550733', 'subgroup_hash': 6181238546636911236, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.(C_2^2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.4.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1536.408640541', 'subgroup_hash': 8944755179417135467, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^5:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.4.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1536.408550734', 'subgroup_hash': 7456160622201197021, 'subgroup_order': 1536, 'subgroup_tex': 'C_4^2.(C_2^2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 1024, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2235204608401505810, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2.C_2^6.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 9110591289533464774, 'subgroup_order': 1024, 'subgroup_tex': 'C_4.C_2^6.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 7477317968349117883, 'subgroup_order': 1024, 'subgroup_tex': '(C_2\\times C_4):D_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 8321630927504865395, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2.C_2^6.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 7518293510052367047, 'subgroup_order': 1024, 'subgroup_tex': '(C_2\\times C_4):D_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 512, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1024.dkd', 'subgroup_hash': 8416105563858596922, 'subgroup_order': 1024, 'subgroup_tex': 'D_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 512, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1024.djm', 'subgroup_hash': 2145159296827724917, 'subgroup_order': 1024, 'subgroup_tex': 'C_2\\times D_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 5165970121695967413, 'subgroup_order': 1024, 'subgroup_tex': 'C_4:D_4.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 8973484681994978496, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2.C_2^5.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 8347012906336527288, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2.C_2^5.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 1816589500778506113, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2.C_2^5.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 512, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 7649488739314710043, 'subgroup_order': 1024, 'subgroup_tex': 'C_4.D_4.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229891000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 512, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 5309449099290160166, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2.C_2^5.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 512, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 5098361455028211862, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2.C_2^5.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 512, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 8156718785496412692, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2.C_2^5.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 7936625845937413593, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2.C_2^5.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 512, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.6.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1024.dgx', 'subgroup_hash': 7936625845937413593, 'subgroup_order': 1024, 'subgroup_tex': 'C_4^2.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 768, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '768.1085082', 'subgroup_hash': 1085082, 'subgroup_order': 768, 'subgroup_tex': '(C_2^2\\times C_4^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090131', 'subgroup_hash': 1090131, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1085205', 'subgroup_hash': 1085205, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090135', 'subgroup_hash': 1090135, 'subgroup_order': 768, 'subgroup_tex': '(C_2\\times C_4^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1083785', 'subgroup_hash': 1083785, 'subgroup_order': 768, 'subgroup_tex': 'C_4^2.(C_2^2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090139', 'subgroup_hash': 1090139, 'subgroup_order': 768, 'subgroup_tex': 'C_4^2.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090135', 'subgroup_hash': 1090135, 'subgroup_order': 768, 'subgroup_tex': '(C_2\\times C_4^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1083510', 'subgroup_hash': 1083510, 'subgroup_order': 768, 'subgroup_tex': 'C_4^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1088659', 'subgroup_hash': 1088659, 'subgroup_order': 768, 'subgroup_tex': '(C_2\\times C_4^2).S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 768, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.8.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090135', 'subgroup_hash': 1090135, 'subgroup_order': 768, 'subgroup_tex': '(C_2\\times C_4^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1089108', 'subgroup_hash': 1089108, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1089093', 'subgroup_hash': 1089093, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1088546', 'subgroup_hash': 1088546, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1084408', 'subgroup_hash': 1084408, 'subgroup_order': 768, 'subgroup_tex': 'C_2\\times C_4^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1087525', 'subgroup_hash': 1087525, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1089093', 'subgroup_hash': 1089093, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1086931', 'subgroup_hash': 1086931, 'subgroup_order': 768, 'subgroup_tex': 'C_4^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1087525', 'subgroup_hash': 1087525, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1087171', 'subgroup_hash': 1087171, 'subgroup_order': 768, 'subgroup_tex': 'C_4^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1085079', 'subgroup_hash': 1085079, 'subgroup_order': 768, 'subgroup_tex': 'C_2^6:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1083783', 'subgroup_hash': 1083783, 'subgroup_order': 768, 'subgroup_tex': 'C_4^2.(C_2^2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1090136', 'subgroup_hash': 1090136, 'subgroup_order': 768, 'subgroup_tex': 'C_2\\times C_4^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1090131', 'subgroup_hash': 1090131, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1088009', 'subgroup_hash': 1088009, 'subgroup_order': 768, 'subgroup_tex': 'C_4^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1085205', 'subgroup_hash': 1085205, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1083785', 'subgroup_hash': 1083785, 'subgroup_order': 768, 'subgroup_tex': 'C_4^2.(C_2^2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1090139', 'subgroup_hash': 1090139, 'subgroup_order': 768, 'subgroup_tex': 'C_4^2.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1090135', 'subgroup_hash': 1090135, 'subgroup_order': 768, 'subgroup_tex': '(C_2\\times C_4^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1090134', 'subgroup_hash': 1090134, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.8.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '768.1086051', 'subgroup_hash': 1086051, 'subgroup_order': 768, 'subgroup_tex': 'C_4^2.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 512, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '512.10493526', 'subgroup_hash': 1823109485990402787, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 512, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '512.6258681', 'subgroup_hash': 8204427275931145422, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 512, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '512.95089', 'subgroup_hash': 703152868451950055, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4^2.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 512, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '512.254130', 'subgroup_hash': 8480418368773449077, 'subgroup_order': 512, 'subgroup_tex': 'C_4^2.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.10482026', 'subgroup_hash': 8389936394607620744, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2.C_2^6.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.10482026', 'subgroup_hash': 8389936394607620744, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2.C_2^6.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 256, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6350498', 'subgroup_hash': 4688377783370066541, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6344776', 'subgroup_hash': 3323202282976551783, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^2.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7529658', 'subgroup_hash': 1671068591183347094, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^3.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.400614', 'subgroup_hash': 7830746387532349218, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^3.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.94226', 'subgroup_hash': 6815266848232445141, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^2.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530060', 'subgroup_hash': 7882903233484254997, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^3.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.400761', 'subgroup_hash': 8612572928748928068, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^2.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6346096', 'subgroup_hash': 6563406352998539771, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times (C_2^2\\times C_4).C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.10482067', 'subgroup_hash': 1709224617210316261, 'subgroup_order': 512, 'subgroup_tex': 'C_2^5:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7529642', 'subgroup_hash': 7137453643301580994, 'subgroup_order': 512, 'subgroup_tex': '(C_2\\times D_4).C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229891459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6344776', 'subgroup_hash': 3323202282976551783, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^2.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6346096', 'subgroup_hash': 6563406352998539771, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times (C_2^2\\times C_4).C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6350498', 'subgroup_hash': 4688377783370066541, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6346096', 'subgroup_hash': 6563406352998539771, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times (C_2^2\\times C_4).C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530060', 'subgroup_hash': 7882903233484254997, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^3.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530060', 'subgroup_hash': 7882903233484254997, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^3.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.10483371', 'subgroup_hash': 8112032011814195978, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6345141', 'subgroup_hash': 2385130641809919280, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6345141', 'subgroup_hash': 2385130641809919280, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6288679', 'subgroup_hash': 1635836254437395213, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530053', 'subgroup_hash': 6592078393715776433, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6255267', 'subgroup_hash': 2619443169651067018, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530053', 'subgroup_hash': 6592078393715776433, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530053', 'subgroup_hash': 6592078393715776433, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.93755', 'subgroup_hash': 5240463764777163299, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.400784', 'subgroup_hash': 1705479759328990181, 'subgroup_order': 512, 'subgroup_tex': 'C_4^2:C_2^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6344767', 'subgroup_hash': 1379696506294818456, 'subgroup_order': 512, 'subgroup_tex': 'C_2^3.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.400602', 'subgroup_hash': 2035415554383603650, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^3.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.10483371', 'subgroup_hash': 8112032011814195978, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6288679', 'subgroup_hash': 1635836254437395213, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419759', 'subgroup_hash': 5864207984865282442, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4:D_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419764', 'subgroup_hash': 6440305935673890735, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.D_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.6345141', 'subgroup_hash': 2385130641809919280, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7408111', 'subgroup_hash': 4551772155935398034, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419795', 'subgroup_hash': 1414708317823511756, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4:D_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419788', 'subgroup_hash': 8483341279705266958, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.D_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7410565', 'subgroup_hash': 6187097775946037045, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419759', 'subgroup_hash': 5864207984865282442, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4:D_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419771', 'subgroup_hash': 3992884642669849923, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.D_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419771', 'subgroup_hash': 3992884642669849923, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.D_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419780', 'subgroup_hash': 2337006264185973032, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4:Q_8.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.59053', 'subgroup_hash': 1801979595069638396, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times (C_2\\times D_4:C_2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.59037', 'subgroup_hash': 7301182332785328753, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times (C_2\\times D_4:C_2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.58989', 'subgroup_hash': 3068676401373676033, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times (C_2\\times D_4:C_2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.58979', 'subgroup_hash': 6115529662367031545, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times (C_2\\times D_4:C_2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7408111', 'subgroup_hash': 4551772155935398034, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530067', 'subgroup_hash': 6627335434885051381, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530096', 'subgroup_hash': 1688833017877239785, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^2.C_2^5.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530067', 'subgroup_hash': 6627335434885051381, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.400813', 'subgroup_hash': 4431984574093365870, 'subgroup_order': 512, 'subgroup_tex': 'C_2^2.C_2^6.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530065', 'subgroup_hash': 8689836347072544817, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2^3.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530058', 'subgroup_hash': 5526727545486539728, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530058', 'subgroup_hash': 5526727545486539728, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530050', 'subgroup_hash': 6209376761179717675, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420049', 'subgroup_hash': 5541581917989114955, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2.D_4^2.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420050', 'subgroup_hash': 824357542665978173, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2.D_4^2.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420067', 'subgroup_hash': 2220484966384102427, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2.D_4^2.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420067', 'subgroup_hash': 2220484966384102427, 'subgroup_order': 512, 'subgroup_tex': 'C_2\\times C_2.D_4^2.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7421336', 'subgroup_hash': 3717343585435044872, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7421336', 'subgroup_hash': 3717343585435044872, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.59223', 'subgroup_hash': 2323877150868405465, 'subgroup_order': 512, 'subgroup_tex': 'D_4.C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.59944', 'subgroup_hash': 4494848556309727787, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229890695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.59898', 'subgroup_hash': 3974828244099893272, 'subgroup_order': 512, 'subgroup_tex': 'D_4.C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7421336', 'subgroup_hash': 3717343585435044872, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7421336', 'subgroup_hash': 3717343585435044872, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530076', 'subgroup_hash': 8222109897935199466, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419015', 'subgroup_hash': 779064748097230029, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.254130', 'subgroup_hash': 8480418368773449077, 'subgroup_order': 512, 'subgroup_tex': 'C_4^2.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229890702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419015', 'subgroup_hash': 779064748097230029, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530076', 'subgroup_hash': 8222109897935199466, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530076', 'subgroup_hash': 8222109897935199466, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.419015', 'subgroup_hash': 779064748097230029, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420060', 'subgroup_hash': 2128154551908325188, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.59752', 'subgroup_hash': 5260648638953525643, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.60343', 'subgroup_hash': 2006353807606903387, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.60315', 'subgroup_hash': 4526424194543930778, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420081', 'subgroup_hash': 3080942358160601456, 'subgroup_order': 512, 'subgroup_tex': '(C_4\\times \\OD_{16}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.59763', 'subgroup_hash': 5861703076455937101, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.60371', 'subgroup_hash': 4919896935252050934, 'subgroup_order': 512, 'subgroup_tex': '(C_4\\times \\OD_{16}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.60329', 'subgroup_hash': 2774682172597644585, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420081', 'subgroup_hash': 3080942358160601456, 'subgroup_order': 512, 'subgroup_tex': '(C_4\\times \\OD_{16}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.59763', 'subgroup_hash': 5861703076455937101, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.60371', 'subgroup_hash': 4919896935252050934, 'subgroup_order': 512, 'subgroup_tex': '(C_4\\times \\OD_{16}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.60329', 'subgroup_hash': 2774682172597644585, 'subgroup_order': 512, 'subgroup_tex': 'C_4^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530076', 'subgroup_hash': 8222109897935199466, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530076', 'subgroup_hash': 8222109897935199466, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.7530076', 'subgroup_hash': 8222109897935199466, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420060', 'subgroup_hash': 2128154551908325188, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229890724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420081', 'subgroup_hash': 3080942358160601456, 'subgroup_order': 512, 'subgroup_tex': '(C_4\\times \\OD_{16}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.12.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '512.420081', 'subgroup_hash': 3080942358160601456, 'subgroup_order': 512, 'subgroup_tex': '(C_4\\times \\OD_{16}):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 384, 'counter': 173, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.16.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18231', 'subgroup_hash': 18231, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 384, 'counter': 174, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.16.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '384.18236', 'subgroup_hash': 18236, 'subgroup_order': 384, 'subgroup_tex': '(C_2\\times C_4^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 384, 'counter': 175, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.16.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18236', 'subgroup_hash': 18236, 'subgroup_order': 384, 'subgroup_tex': '(C_2\\times C_4^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 176, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.16.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18135', 'subgroup_hash': 18135, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.18158', 'subgroup_hash': 18158, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.20051', 'subgroup_hash': 20051, 'subgroup_order': 384, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 229890732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.18198', 'subgroup_hash': 18198, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.18167', 'subgroup_hash': 18167, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17948', 'subgroup_hash': 17948, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17948', 'subgroup_hash': 17948, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17861', 'subgroup_hash': 17861, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17949', 'subgroup_hash': 17949, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5658', 'subgroup_hash': 5658, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.18167', 'subgroup_hash': 18167, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17861', 'subgroup_hash': 17861, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17861', 'subgroup_hash': 17861, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890743
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5734', 'subgroup_hash': 5734, 'subgroup_order': 384, 'subgroup_tex': 'C_4^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 229890745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5623', 'subgroup_hash': 5623, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.20163', 'subgroup_hash': 20163, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 229890747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17948', 'subgroup_hash': 17948, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17949', 'subgroup_hash': 17949, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17949', 'subgroup_hash': 17949, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17948', 'subgroup_hash': 17948, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17949', 'subgroup_hash': 17949, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5797', 'subgroup_hash': 5797, 'subgroup_order': 384, 'subgroup_tex': 'C_4^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 229890753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5660', 'subgroup_hash': 5660, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5677', 'subgroup_hash': 5677, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17949', 'subgroup_hash': 17949, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5557', 'subgroup_hash': 5557, 'subgroup_order': 384, 'subgroup_tex': 'C_4\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 229890759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5660', 'subgroup_hash': 5660, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.5558', 'subgroup_hash': 5558, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 229890761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17948', 'subgroup_hash': 17948, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17949', 'subgroup_hash': 17949, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.17949', 'subgroup_hash': 17949, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 192, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.18235', 'subgroup_hash': 18235, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 192, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.591', 'subgroup_hash': 591, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2.(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 229890766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 192, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.18134', 'subgroup_hash': 18134, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 192, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.16.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18135', 'subgroup_hash': 18135, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229890769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 256, 'counter': 211, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.29630', 'subgroup_hash': 29630, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 256, 'counter': 212, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '256.55745', 'subgroup_hash': 55745, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 256, 'counter': 213, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.24.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.55999', 'subgroup_hash': 55999, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 256, 'counter': 214, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.24.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.12061', 'subgroup_hash': 12061, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 256, 'counter': 215, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.24.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.1518', 'subgroup_hash': 1518, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53373', 'subgroup_hash': 53373, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53366', 'subgroup_hash': 53366, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53370', 'subgroup_hash': 53370, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53371', 'subgroup_hash': 53371, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.54086', 'subgroup_hash': 54086, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.54090', 'subgroup_hash': 54090, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.54091', 'subgroup_hash': 54091, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.54086', 'subgroup_hash': 54086, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53383', 'subgroup_hash': 53383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.56089', 'subgroup_hash': 56089, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.55783', 'subgroup_hash': 55783, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.55712', 'subgroup_hash': 55712, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53366', 'subgroup_hash': 53366, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53371', 'subgroup_hash': 53371, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53056', 'subgroup_hash': 53056, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53062', 'subgroup_hash': 53062, 'subgroup_order': 256, 'subgroup_tex': '\\OD_{16}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53380', 'subgroup_hash': 53380, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.55751', 'subgroup_hash': 55751, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53371', 'subgroup_hash': 53371, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.55783', 'subgroup_hash': 55783, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53366', 'subgroup_hash': 53366, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53371', 'subgroup_hash': 53371, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53062', 'subgroup_hash': 53062, 'subgroup_order': 256, 'subgroup_tex': '\\OD_{16}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53366', 'subgroup_hash': 53366, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.16383', 'subgroup_hash': 16383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53384', 'subgroup_hash': 53384, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.26333', 'subgroup_hash': 26333, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.14003', 'subgroup_hash': 14003, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.26536', 'subgroup_hash': 26536, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.16383', 'subgroup_hash': 16383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.14203', 'subgroup_hash': 14203, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14003', 'subgroup_hash': 14003, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.16608', 'subgroup_hash': 16608, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 229890812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.16383', 'subgroup_hash': 16383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.14203', 'subgroup_hash': 14203, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53383', 'subgroup_hash': 53383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53382', 'subgroup_hash': 53382, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53382', 'subgroup_hash': 53382, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.26331', 'subgroup_hash': 26331, 'subgroup_order': 256, 'subgroup_tex': '(C_2^4\\times C_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.26331', 'subgroup_hash': 26331, 'subgroup_order': 256, 'subgroup_tex': '(C_2^4\\times C_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.55712', 'subgroup_hash': 55712, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.56076', 'subgroup_hash': 56076, 'subgroup_order': 256, 'subgroup_tex': 'D_8:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.56076', 'subgroup_hash': 56076, 'subgroup_order': 256, 'subgroup_tex': 'D_8:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53373', 'subgroup_hash': 53373, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53370', 'subgroup_hash': 53370, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53080', 'subgroup_hash': 53080, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53080', 'subgroup_hash': 53080, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.53366', 'subgroup_hash': 53366, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '256.56076', 'subgroup_hash': 56076, 'subgroup_order': 256, 'subgroup_tex': 'D_8:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13609', 'subgroup_hash': 13609, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13609', 'subgroup_hash': 13609, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53382', 'subgroup_hash': 53382, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26331', 'subgroup_hash': 26331, 'subgroup_order': 256, 'subgroup_tex': '(C_2^4\\times C_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26331', 'subgroup_hash': 26331, 'subgroup_order': 256, 'subgroup_tex': '(C_2^4\\times C_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13951', 'subgroup_hash': 13951, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times C_8):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53455', 'subgroup_hash': 53455, 'subgroup_order': 256, 'subgroup_tex': '\\OD_{16}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13982', 'subgroup_hash': 13982, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times D_8):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53400', 'subgroup_hash': 53400, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53168', 'subgroup_hash': 53168, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13987', 'subgroup_hash': 13987, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13854', 'subgroup_hash': 13854, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13390', 'subgroup_hash': 13390, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.10434', 'subgroup_hash': 10434, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53380', 'subgroup_hash': 53380, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55702', 'subgroup_hash': 55702, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55751', 'subgroup_hash': 55751, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53370', 'subgroup_hash': 53370, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53373', 'subgroup_hash': 53373, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.56076', 'subgroup_hash': 56076, 'subgroup_order': 256, 'subgroup_tex': 'D_8:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53080', 'subgroup_hash': 53080, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26536', 'subgroup_hash': 26536, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53624', 'subgroup_hash': 53624, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53370', 'subgroup_hash': 53370, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53370', 'subgroup_hash': 53370, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14195', 'subgroup_hash': 14195, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26342', 'subgroup_hash': 26342, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times C_4^2):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13934', 'subgroup_hash': 13934, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26342', 'subgroup_hash': 26342, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times C_4^2):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26342', 'subgroup_hash': 26342, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times C_4^2):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.10624', 'subgroup_hash': 10624, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.10723', 'subgroup_hash': 10723, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26353', 'subgroup_hash': 26353, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2^2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229890868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53373', 'subgroup_hash': 53373, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26344', 'subgroup_hash': 26344, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13996', 'subgroup_hash': 13996, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times C_8):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26355', 'subgroup_hash': 26355, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2^2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229890872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16383', 'subgroup_hash': 16383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16398', 'subgroup_hash': 16398, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53373', 'subgroup_hash': 53373, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26344', 'subgroup_hash': 26344, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53455', 'subgroup_hash': 53455, 'subgroup_order': 256, 'subgroup_tex': '\\OD_{16}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53373', 'subgroup_hash': 53373, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16511', 'subgroup_hash': 16511, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53370', 'subgroup_hash': 53370, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16514', 'subgroup_hash': 16514, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14067', 'subgroup_hash': 14067, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53384', 'subgroup_hash': 53384, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53384', 'subgroup_hash': 53384, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26333', 'subgroup_hash': 26333, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26333', 'subgroup_hash': 26333, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.56076', 'subgroup_hash': 56076, 'subgroup_order': 256, 'subgroup_tex': 'D_8:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53455', 'subgroup_hash': 53455, 'subgroup_order': 256, 'subgroup_tex': '\\OD_{16}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13987', 'subgroup_hash': 13987, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53168', 'subgroup_hash': 53168, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53366', 'subgroup_hash': 53366, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53400', 'subgroup_hash': 53400, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53455', 'subgroup_hash': 53455, 'subgroup_order': 256, 'subgroup_tex': '\\OD_{16}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13982', 'subgroup_hash': 13982, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times D_8):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13609', 'subgroup_hash': 13609, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13982', 'subgroup_hash': 13982, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times D_8):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53366', 'subgroup_hash': 53366, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13987', 'subgroup_hash': 13987, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53168', 'subgroup_hash': 53168, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13854', 'subgroup_hash': 13854, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13390', 'subgroup_hash': 13390, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13854', 'subgroup_hash': 13854, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16398', 'subgroup_hash': 16398, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53455', 'subgroup_hash': 53455, 'subgroup_order': 256, 'subgroup_tex': '\\OD_{16}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53370', 'subgroup_hash': 53370, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16514', 'subgroup_hash': 16514, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53624', 'subgroup_hash': 53624, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16383', 'subgroup_hash': 16383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53455', 'subgroup_hash': 53455, 'subgroup_order': 256, 'subgroup_tex': '\\OD_{16}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16511', 'subgroup_hash': 16511, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16398', 'subgroup_hash': 16398, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16511', 'subgroup_hash': 16511, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16383', 'subgroup_hash': 16383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13934', 'subgroup_hash': 13934, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14195', 'subgroup_hash': 14195, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16514', 'subgroup_hash': 16514, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14067', 'subgroup_hash': 14067, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14067', 'subgroup_hash': 14067, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53383', 'subgroup_hash': 53383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53366', 'subgroup_hash': 53366, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53371', 'subgroup_hash': 53371, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26332', 'subgroup_hash': 26332, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26340', 'subgroup_hash': 26340, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26343', 'subgroup_hash': 26343, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53383', 'subgroup_hash': 53383, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55732', 'subgroup_hash': 55732, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26332', 'subgroup_hash': 26332, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53373', 'subgroup_hash': 53373, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53370', 'subgroup_hash': 53370, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53056', 'subgroup_hash': 53056, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fu2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53382', 'subgroup_hash': 53382, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53380', 'subgroup_hash': 53380, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26329', 'subgroup_hash': 26329, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55759', 'subgroup_hash': 55759, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.FZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55706', 'subgroup_hash': 55706, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53380', 'subgroup_hash': 53380, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26329', 'subgroup_hash': 26329, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55706', 'subgroup_hash': 55706, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55751', 'subgroup_hash': 55751, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55683', 'subgroup_hash': 55683, 'subgroup_order': 256, 'subgroup_tex': 'C_2^2\\times D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53384', 'subgroup_hash': 53384, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229890948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26532', 'subgroup_hash': 26532, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26532', 'subgroup_hash': 26532, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.13984', 'subgroup_hash': 13984, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times D_8):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16401', 'subgroup_hash': 16401, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26532', 'subgroup_hash': 26532, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11464', 'subgroup_hash': 11464, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11462', 'subgroup_hash': 11462, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53342', 'subgroup_hash': 53342, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26536', 'subgroup_hash': 26536, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54091', 'subgroup_hash': 54091, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26533', 'subgroup_hash': 26533, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6547', 'subgroup_hash': 6547, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.GZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26535', 'subgroup_hash': 26535, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54086', 'subgroup_hash': 54086, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6551', 'subgroup_hash': 6551, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26536', 'subgroup_hash': 26536, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11466', 'subgroup_hash': 11466, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6569', 'subgroup_hash': 6569, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2^2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229890975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26533', 'subgroup_hash': 26533, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26553', 'subgroup_hash': 26553, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6547', 'subgroup_hash': 6547, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26533', 'subgroup_hash': 26533, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16398', 'subgroup_hash': 16398, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times \\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11966', 'subgroup_hash': 11966, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26550', 'subgroup_hash': 26550, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26535', 'subgroup_hash': 26535, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6563', 'subgroup_hash': 6563, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2^2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229890986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6555', 'subgroup_hash': 6555, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26536', 'subgroup_hash': 26536, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26536', 'subgroup_hash': 26536, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26535', 'subgroup_hash': 26535, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11966', 'subgroup_hash': 11966, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229890994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26550', 'subgroup_hash': 26550, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26535', 'subgroup_hash': 26535, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54086', 'subgroup_hash': 54086, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54090', 'subgroup_hash': 54090, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229890998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.HZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6555', 'subgroup_hash': 6555, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229890999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6559', 'subgroup_hash': 6559, 'subgroup_order': 256, 'subgroup_tex': 'C_2\\times C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.ID', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18735', 'subgroup_hash': 18735, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16860', 'subgroup_hash': 16860, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.II', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26347', 'subgroup_hash': 26347, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2^2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5743', 'subgroup_hash': 5743, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18184', 'subgroup_hash': 18184, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18735', 'subgroup_hash': 18735, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16860', 'subgroup_hash': 16860, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26347', 'subgroup_hash': 26347, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2^2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5706', 'subgroup_hash': 5706, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times D_4).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1457', 'subgroup_hash': 1457, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times \\OD_{16}):C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5743', 'subgroup_hash': 5743, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18735', 'subgroup_hash': 18735, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.IZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16860', 'subgroup_hash': 16860, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1457', 'subgroup_hash': 1457, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times \\OD_{16}):C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18184', 'subgroup_hash': 18184, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18735', 'subgroup_hash': 18735, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16860', 'subgroup_hash': 16860, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5706', 'subgroup_hash': 5706, 'subgroup_order': 256, 'subgroup_tex': '(C_2^2\\times D_4).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53387', 'subgroup_hash': 53387, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53387', 'subgroup_hash': 53387, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26336', 'subgroup_hash': 26336, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53387', 'subgroup_hash': 53387, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53387', 'subgroup_hash': 53387, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26336', 'subgroup_hash': 26336, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55999', 'subgroup_hash': 55999, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55999', 'subgroup_hash': 55999, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55999', 'subgroup_hash': 55999, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16860', 'subgroup_hash': 16860, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18184', 'subgroup_hash': 18184, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16860', 'subgroup_hash': 16860, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18184', 'subgroup_hash': 18184, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18735', 'subgroup_hash': 18735, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18735', 'subgroup_hash': 18735, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18184', 'subgroup_hash': 18184, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.18184', 'subgroup_hash': 18184, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.JZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.17460', 'subgroup_hash': 17460, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.17460', 'subgroup_hash': 17460, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.17460', 'subgroup_hash': 17460, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.17460', 'subgroup_hash': 17460, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.15887', 'subgroup_hash': 15887, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.15887', 'subgroup_hash': 15887, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16870', 'subgroup_hash': 16870, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5699', 'subgroup_hash': 5699, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11515', 'subgroup_hash': 11515, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1428', 'subgroup_hash': 1428, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5753', 'subgroup_hash': 5753, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16870', 'subgroup_hash': 16870, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5699', 'subgroup_hash': 5699, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11515', 'subgroup_hash': 11515, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1428', 'subgroup_hash': 1428, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5753', 'subgroup_hash': 5753, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.KZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.15887', 'subgroup_hash': 15887, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.17460', 'subgroup_hash': 17460, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.15887', 'subgroup_hash': 15887, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6550', 'subgroup_hash': 6550, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6552', 'subgroup_hash': 6552, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26558', 'subgroup_hash': 26558, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5766', 'subgroup_hash': 5766, 'subgroup_order': 256, 'subgroup_tex': '(C_2\\times C_4^2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.12061', 'subgroup_hash': 12061, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26558', 'subgroup_hash': 26558, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1518', 'subgroup_hash': 1518, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5766', 'subgroup_hash': 5766, 'subgroup_order': 256, 'subgroup_tex': '(C_2\\times C_4^2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.23484', 'subgroup_hash': 23484, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.24064', 'subgroup_hash': 24064, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.23484', 'subgroup_hash': 23484, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.23484', 'subgroup_hash': 23484, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6573', 'subgroup_hash': 6573, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times \\OD_{16}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6567', 'subgroup_hash': 6567, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times \\OD_{16}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.24064', 'subgroup_hash': 24064, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6550', 'subgroup_hash': 6550, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6556', 'subgroup_hash': 6556, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6556', 'subgroup_hash': 6556, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6562', 'subgroup_hash': 6562, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.485', 'subgroup_hash': 485, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.LZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.488', 'subgroup_hash': 488, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.474', 'subgroup_hash': 474, 'subgroup_order': 256, 'subgroup_tex': '(C_2\\times D_4).C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.470', 'subgroup_hash': 470, 'subgroup_order': 256, 'subgroup_tex': '(C_2\\times C_4^2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.ME', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26558', 'subgroup_hash': 26558, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5766', 'subgroup_hash': 5766, 'subgroup_order': 256, 'subgroup_tex': '(C_2\\times C_4^2).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.15887', 'subgroup_hash': 15887, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.17460', 'subgroup_hash': 17460, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.ML', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.15887', 'subgroup_hash': 15887, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.23484', 'subgroup_hash': 23484, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.24064', 'subgroup_hash': 24064, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.23484', 'subgroup_hash': 23484, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.23484', 'subgroup_hash': 23484, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.24064', 'subgroup_hash': 24064, 'subgroup_order': 256, 'subgroup_tex': 'C_4^3:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ms1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26347', 'subgroup_hash': 26347, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2^2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26347', 'subgroup_hash': 26347, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2^2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53376', 'subgroup_hash': 53376, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53387', 'subgroup_hash': 53387, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.MZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53387', 'subgroup_hash': 53387, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.my1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26336', 'subgroup_hash': 26336, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.mz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53387', 'subgroup_hash': 53387, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.na1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.53387', 'subgroup_hash': 53387, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.ND', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26336', 'subgroup_hash': 26336, 'subgroup_order': 256, 'subgroup_tex': '(D_4\\times C_2^3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55999', 'subgroup_hash': 55999, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55999', 'subgroup_hash': 55999, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ne1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55999', 'subgroup_hash': 55999, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55999', 'subgroup_hash': 55999, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ng1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ni1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26541', 'subgroup_hash': 26541, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16870', 'subgroup_hash': 16870, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.no1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11515', 'subgroup_hash': 11515, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.np1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.11515', 'subgroup_hash': 11515, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ns1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16870', 'subgroup_hash': 16870, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26534', 'subgroup_hash': 26534, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6552', 'subgroup_hash': 6552, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.NZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ny1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6550', 'subgroup_hash': 6550, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.nz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.12061', 'subgroup_hash': 12061, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26558', 'subgroup_hash': 26558, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ob1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26558', 'subgroup_hash': 26558, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.od1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6567', 'subgroup_hash': 6567, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times \\OD_{16}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6556', 'subgroup_hash': 6556, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.of1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6573', 'subgroup_hash': 6573, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times \\OD_{16}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.og1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6550', 'subgroup_hash': 6550, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ok1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.12061', 'subgroup_hash': 12061, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 229891186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.ON', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ol1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26558', 'subgroup_hash': 26558, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 128, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.om1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.on1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54098', 'subgroup_hash': 54098, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.op1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6562', 'subgroup_hash': 6562, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6556', 'subgroup_hash': 6556, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.or1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26545', 'subgroup_hash': 26545, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.os1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26545', 'subgroup_hash': 26545, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ot1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26545', 'subgroup_hash': 26545, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ou1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26545', 'subgroup_hash': 26545, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ov1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ow1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.OZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ow2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ox1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.oz2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26531', 'subgroup_hash': 26531, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6661', 'subgroup_hash': 6661, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6665', 'subgroup_hash': 6665, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ph1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6665', 'subgroup_hash': 6665, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6663', 'subgroup_hash': 6663, 'subgroup_order': 256, 'subgroup_tex': '(C_4\\times C_8).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6665', 'subgroup_hash': 6665, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.24.PO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.pk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.6665', 'subgroup_hash': 6665, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 229891218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 192, 'counter': 616, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.32.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C5'], '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: 229891219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1537', 'subgroup_hash': 1537, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1000', 'subgroup_hash': 1000, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1537', 'subgroup_hash': 1537, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1469', 'subgroup_hash': 1469, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1002', 'subgroup_hash': 1002, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 229891228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1470', 'subgroup_hash': 1470, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 229891229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.992', 'subgroup_hash': 992, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 229891231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1000', 'subgroup_hash': 1000, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1002', 'subgroup_hash': 1002, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1001', 'subgroup_hash': 1001, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1002', 'subgroup_hash': 1002, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1000', 'subgroup_hash': 1000, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1002', 'subgroup_hash': 1002, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1008', 'subgroup_hash': 1008, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.956', 'subgroup_hash': 956, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.185', 'subgroup_hash': 185, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1002', 'subgroup_hash': 1002, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 64, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.188', 'subgroup_hash': 188, 'subgroup_order': 192, 'subgroup_tex': 'C_4\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 229891257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.182', 'subgroup_hash': 182, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1000', 'subgroup_hash': 1000, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1008', 'subgroup_hash': 1008, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1002', 'subgroup_hash': 1002, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.956', 'subgroup_hash': 956, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1002', 'subgroup_hash': 1002, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.956', 'subgroup_hash': 956, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.32.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.956', 'subgroup_hash': 956, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 229891273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 666, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.48.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.2172', 'subgroup_hash': 2172, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 667, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.48.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2172', 'subgroup_hash': 2172, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891275
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 128, 'counter': 668, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.48.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.997', 'subgroup_hash': 997, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\times C_4^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 669, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.48.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2258', 'subgroup_hash': 2258, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 128, 'counter': 670, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.48.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.e1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1599', 'subgroup_hash': 1599, 'subgroup_order': 128, 'subgroup_tex': 'C_4^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 671, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.48.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.f1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.2281', 'subgroup_hash': 2281, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 672, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.48.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.g1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2281', 'subgroup_hash': 2281, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.64.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.64.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891283
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 64, 'counter': 675, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.96.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.192', 'subgroup_hash': 192, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 676, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.96.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 677, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.96.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891286
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 64, 'counter': 678, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.96.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.55', 'subgroup_hash': 55, 'subgroup_order': 64, 'subgroup_tex': 'C_4^3', 'supersolvable': True, 'sylow': 0}
  • id: 229891287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 679, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.96.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.e1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.209', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 209, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6'], '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: 229891289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.128.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.c1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.128.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.e1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.128.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.e1.NC3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.128.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.g1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891293
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 684, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.192.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.955', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 955, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 229891294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.192.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.a1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.192.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.a1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.192.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.a1.NC3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.192.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.a1.NC4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.192.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.a1.NC5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.192.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.a1.NC6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 229891301
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 691, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.192.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1472', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1472, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891302
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 692, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.192.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1537', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1537, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891303
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 693, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.192.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1472', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1472, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.256.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.a1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.256.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.a1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 229891306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.256.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.c1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.256.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.c1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.256.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.d1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.256.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.d1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891312
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 16, 'counter': 700, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.384.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '384.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '384.17948', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17948, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:S_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 229891313
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 701, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.384.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '384.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '384.17948', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17948, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:S_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 229891314
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 702, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.384.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '384.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '384.20051', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 20051, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,\\mathbb{Z}/4):C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 229891315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1.NC3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1.NC4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC7', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC8', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC9', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC10', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC11', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC16', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC17', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC18', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC19', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC20', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC21', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC22', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC23', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC24', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC25', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC26', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC27', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.384.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.NC28', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': 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: 229891346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.512.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.c1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.512.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.c1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.512.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.d1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.512.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.d1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.512.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.d1.NC5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.512.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.d1.NC6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.512.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.d1.NC7', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.512.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '512.d1.NC8', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 229891354
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1024, 'characteristic': True, 'core_order': 8, 'counter': 739, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.768.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '768.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '768.1087581', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1087581, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\wr D_6', 'simple': False, 'solvable': True, 'special_labels': ['S'], '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: 229891356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 740, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.768.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '768.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '768.1089108', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1089108, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5:S_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: 229891357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 741, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.768.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '768.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '768.1087581', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1087581, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\wr D_6', '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: 229891358
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891360
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891362
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891363
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891364
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC7', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891365
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC8', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891367
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC9', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891368
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC10', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891369
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC11', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC12', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC13', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891372
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.h1.NC14', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC7', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC8', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC9', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC10', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC11', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.768.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '768.j1.NC12', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 768, 'quotient_simple': 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: 229891386
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1024.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1024.a1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1024, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 229891387
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1024.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1024.a1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1024, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 229891389
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1024.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1024.a1.NC3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1024, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 229891390
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1024, 'characteristic': True, 'core_order': 4, 'counter': 771, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '6144.ze.1536.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1536.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1536.408610984', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1245632016200004786, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1536, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^7:D_6', 'simple': False, 'solvable': True, 'special_labels': ['D3', 'C8'], '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: 229891391
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.j1.NC8', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891392
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.j1.NC9', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891393
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.j1.NC10', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891394
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.j1.NC11', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891395
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 768, 'characteristic': False, 'core_order': 2, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891397
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891398
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891400
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891401
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891402
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC7', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891403
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 512, 'characteristic': False, 'core_order': 1, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC8', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891404
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 512, 'characteristic': False, 'core_order': 2, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC9', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891405
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC10', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891406
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC11', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891407
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC12', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891408
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC13', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891409
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC14', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891411
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC15', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891412
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC16', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891413
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC17', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC18', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC19', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC20', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891417
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC21', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891418
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC22', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891419
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC23', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891420
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC24', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891423
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC25', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891424
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC26', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891425
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC27', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC28', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891427
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.m1.NC29', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891428
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.n1.NC8', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891429
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.n1.NC9', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.n1.NC10', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891431
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.ze.1536.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1536.n1.NC11', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1536, 'quotient_simple': 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: 229891432
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 809, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '6144.ze.2048.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2048.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2048, '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: 229891434
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': True, 'central_factor': False, 'centralizer_order': 6144, 'characteristic': True, 'core_order': 2, 'counter': 810, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '6144.ze.3072.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '3072.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3072.bgb', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7983714371117797868, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 3072, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4^3:(C_2\\times S_4)', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 229891435
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 811, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.c1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891436
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 812, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.c1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891437
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 813, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.c1.NC3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891438
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 768, 'characteristic': False, 'core_order': 1, 'counter': 814, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.e1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891439
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 815, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.e1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891440
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 512, 'characteristic': False, 'core_order': 1, 'counter': 816, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.e1.NC4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891441
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 817, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.e1.NC6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891442
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2048, 'characteristic': False, 'core_order': 1, 'counter': 818, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.h1.NC1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891443
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 1536, 'characteristic': False, 'core_order': 1, 'counter': 819, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.h1.NC2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891445
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 820, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.h1.NC7', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891446
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 821, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '6144.ze.3072.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3072.h1.NC8', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3072, '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: 229891447
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '6144.ze', 'ambient_counter': 655, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:(C_2^2\\times S_4)', 'central': True, 'central_factor': False, 'centralizer_order': 6144, 'characteristic': True, 'core_order': 1, 'counter': 822, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '6144.ze.6144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6144.a1.N', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '6144.ze', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4158378184127417885, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 6144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4^3:(C_2^2\\times S_4)', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D4', 'C9'], '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: 229891350
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '512.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.F'], 'contains': ['1024.B', '1536.C'], 'core': '6144.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [122000787877212840, 25852138759281662150272, 216288449198190123592319], 'label': '6144.ze.512.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '512.d1.NC5', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.E', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891351
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '512.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.C', '256.E'], 'contains': ['1024.B', '1536.D'], 'core': '3072.A', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [25852138759281662150272, 25903229683158464681647, 216288449198190123592319], 'label': '6144.ze.512.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '512.d1.NC6', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.F', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891352
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '512.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.D'], 'contains': ['1024.C', '1536.BE'], 'core': '6144.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [122000787877212840, 242089374992119825754737, 53952156953721766679632], 'label': '6144.ze.512.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '512.d1.NC7', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.G', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891353
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '512.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['256.C'], 'contains': ['1024.C', '1536.BG'], 'core': '3072.A', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [242089374992119825754737, 25903229683158464681647, 53952156953721766679632], 'label': '6144.ze.512.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '512.d1.NC8', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.H', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891378
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.O', '384.P', '384.Q', '384.R'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [122000787877207687, 51212590061910698296, 25903364133006332138897], 'label': '6144.ze.768.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC5', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.V', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891379
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.D', '384.G', '384.S', '384.T'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25852138759281662150272, 25903107681056726364840, 79804051672210232750640], 'label': '6144.ze.768.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC6', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.W', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891380
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.E', '384.F', '384.T', '384.U'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25852138759281662150272, 79804051673524173688447, 25903107681056726364840], 'label': '6144.ze.768.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC7', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.X', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891381
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.D', '384.E', '384.X', '384.Y'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [51468697530548501041, 25852394837410748380801, 122002101738321960], 'label': '6144.ze.768.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC8', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.Y', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891382
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.F', '384.G', '384.V', '384.W'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [122000787877207687, 51347041223585195521, 25852273204830834960126], 'label': '6144.ze.768.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC9', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.Z', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891383
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.F', '384.G', '384.Z', '384.BA'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [51468697530548501041, 122002101738321960, 25852017097362197157143], 'label': '6144.ze.768.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.J', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC10', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BA', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891384
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.D', '384.E', '384.BB', '384.BC'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [51468697530548501041, 122002101738321960, 25852138383991612855801], 'label': '6144.ze.768.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.J', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC11', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BB', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891385
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['384.BD', '384.BE'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [133970303628669208769263, 53952156953721766679632, 79855398717726110999616], 'label': '6144.ze.768.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC12', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.BC', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891295
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['384.F', '384.G', '384.M', '384.T', '384.W', '384.BA'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 51212590061910698296, 25903229681844523008000, 377741362626800062], 'label': '6144.ze.192.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '192.a1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.C', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891296
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['384.F', '384.N', '384.U', '384.V', '384.Z'], 'core': '3072.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 51212590061910698296, 25903229683158464681647, 377741362626800062], 'label': '6144.ze.192.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '192.a1.NC3', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.D', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891297
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.B'], 'contains': ['384.D', '384.H', '384.S', '384.Y', '384.BB'], 'core': '3072.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 25903229683158464681647, 51091299166851820921, 377740048764960017], 'label': '6144.ze.192.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '192.a1.NC4', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.E', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229890644
    {'ambient': '6144.ze', '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': '3072.A', 'complements': ['6144.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.A', '2.B', '2.C', '2.D', '2.E', '2.F', '2.G', '2.H', '3.a1', '4.O'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [698, 4754, 770, 5326], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 377740048764960017, 51090957482037557056, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.1.a1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.A', '2.B', '2.C', '2.D', '2.E', '2.F', '2.G', '2.H'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890645
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.A', '6.B', '6.C', '6.D', '6.E', '6.F', '6.G', '6.H', '6.I', '6.J', '6.K', '6.L', '6.M', '6.N', '6.O', '6.P', '6.Q'], 'core': '6.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5269, -1, 5587, -1], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 377740048764960017, 51090957482037557056, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.3.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890646
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.BV', '24.BX', '24.BZ', '24.CB', '24.CD', '24.CL', '24.CP', '24.EE', '24.EF', '24.EI', '24.EK', '24.ET', '24.EW', '24.EY', '24.FA', '24.KB', '24.KD'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8142, -1, 8996, -1], 'generators': [25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 377740048764960017, 51090957482037557056, 53952413034673736392198, 4097467157062], 'label': '6144.ze.12.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.x1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.X', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890647
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.BW', '24.BX', '24.CA', '24.CK', '24.CL', '24.CM', '24.CO', '24.EL', '24.EM', '24.EN', '24.ES', '24.FB', '24.FC', '24.FD', '24.FG', '24.KE', '24.KF'], 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [9301, -1, 9222, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.y1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Y', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890648
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.BY', '24.BZ', '24.CA', '24.CN', '24.CO', '24.CP', '24.CQ', '24.EO', '24.EP', '24.EQ', '24.ER', '24.FE', '24.FF', '24.FH', '24.FI', '24.KG', '24.KH'], 'core': '48.C', 'coset_action_label': None, 'count': 6, 'diagramx': [9141, -1, 9288, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.12.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.z1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Z', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890737
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B', '8.L', '8.P', '8.Q'], 'contains': ['32.K', '32.R', '32.BC', '32.BP'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1877, -1, 452, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056], 'label': '6144.ze.16.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.k1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.K', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229890649
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F', '6.H', '6.I'], 'contains': ['24.BQ', '24.BS', '24.CT', '24.CV', '24.DE', '24.GH', '24.GQ', '24.GX', '24.KI', '24.KJ', '24.NM', '24.NN'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5578, -1, 5350, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.ba1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BA', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890650
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.A', '6.H', '6.J'], 'contains': ['24.CM', '24.CR', '24.CT', '24.DA', '24.DJ', '24.GP', '24.GR', '24.HD', '24.KN', '24.KU', '24.NQ', '24.NT'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [6445, -1, 6256, -1], 'generators': [54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108118542983424833692672], 'label': '6144.ze.12.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bb1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BB', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229890651
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G', '6.H', '6.K'], 'contains': ['24.CF', '24.CH', '24.CT', '24.DB', '24.DH', '24.GO', '24.GS', '24.HF', '24.KO', '24.KW', '24.NR', '24.NV'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5921, -1, 5847, -1], 'generators': [54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.12.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bc1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BC', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890652
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F', '6.J', '6.K'], 'contains': ['24.BR', '24.BT', '24.CT', '24.DC', '24.DG', '24.GJ', '24.GT', '24.HI', '24.KK', '24.KP', '24.NP', '24.NS'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5359, -1, 5110, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bd1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BD', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890653
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.A', '6.I', '6.K'], 'contains': ['24.CQ', '24.CR', '24.CT', '24.DD', '24.DI', '24.KQ', '24.KV'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5853, -1, 5916, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.12.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.be1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BE', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890654
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G', '6.I', '6.J'], 'contains': ['24.CG', '24.CI', '24.CT', '24.DF', '24.DK', '24.KR', '24.KX'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4994, -1, 5063, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51468697530548501041, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bf1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BF', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890655
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G'], 'contains': ['24.CC', '24.CE', '24.CF', '24.CI', '24.CU', '24.DL', '24.DN', '24.GM', '24.GN', '24.GU', '24.HJ', '24.KL', '24.KS', '24.NO', '24.NU'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1276, -1, 2547, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 256115864664974016, 53952413034673736392198, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.12.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '12.bg1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BG', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229890656
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.BD'], 'conjugacy_class_count': 1, 'contained_in': ['2.A', '2.B', '2.C'], 'contains': ['8.A', '8.C', '8.T', '8.Y', '12.A', '16.E', '16.G', '16.H'], 'core': '4.A', 'coset_action_label': None, 'count': 1, 'diagramx': [1815, 1117, 921, 3014], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.4.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': ['2.A', '2.B', '2.C'], 'normal_contains': ['8.A', '8.C', '12.A'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '2500.l', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.A', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890657
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G'], 'contains': ['24.CD', '24.CE', '24.CG', '24.CH', '24.CU', '24.DM', '24.DO', '24.KM', '24.KT'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1478, -1, 2405, -1], 'generators': [25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 53952413034673736392198, 4097467157062, 108118165243376109012342, 51468697530548501041], 'label': '6144.ze.12.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '12.bh1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BH', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229890658
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.H', '6.L'], 'contains': ['24.CV', '24.CX', '24.DA', '24.DB', '24.DT', '24.ED', '24.EE', '24.EN', '24.EP', '24.GW', '24.HA', '24.HX', '24.HY', '24.KZ', '24.LC', '24.MI', '24.ML', '24.NX', '24.NZ', '24.OP', '24.OQ'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [7255, -1, 6884, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bi1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BI', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890659
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.I', '6.M'], 'contains': ['24.CV', '24.CY', '24.DD', '24.DF', '24.DY', '24.EF', '24.EG', '24.ER', '24.ES', '24.LA', '24.LD', '24.MJ', '24.MM'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': [7487, -1, 7589, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.12.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bj1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BJ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890660
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.H', '6.M'], 'contains': ['24.CV', '24.DH', '24.DJ', '24.GY', '24.LE', '24.OA'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6076, -1, 6210, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108118542983424833692672, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bk1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BK', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890661
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.I', '6.L'], 'contains': ['24.CV', '24.DI', '24.DK', '24.HB', '24.LF', '24.NY'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5263, -1, 5250, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108118542993128400914047, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bl1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BL', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890662
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.CW', '24.CX', '24.CY', '24.DP', '24.DQ', '24.DV', '24.DX', '24.EH', '24.EI', '24.EJ', '24.EK', '24.EL', '24.EM', '24.EO', '24.EQ', '24.LB', '24.MK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9202, -1, 8771, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.12.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.bm1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BM', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890738
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.D', '8.M'], 'contains': ['32.H', '32.U', '32.BD', '32.BQ'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': [91, -1, 603, -1], 'generators': [122000787877207687, 187973563958306240457616, 108118287248261452641239, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480, 378111052493809927], 'label': '6144.ze.16.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.M', 'old_label': '16.l1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.L', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 229890663
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.J', '6.N'], 'contains': ['24.DA', '24.DC', '24.DF', '24.DU', '24.DV', '24.ET', '24.EU', '24.FD', '24.FI', '24.LN', '24.LQ', '24.MN', '24.MQ'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [7711, -1, 7708, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bn1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BN', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890664
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.H', '6.N'], 'contains': ['24.DA', '24.DE', '24.DH', '24.HE', '24.LR', '24.OH'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [6057, -1, 5892, -1], 'generators': [54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.12.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bo1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BO', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890665
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.J', '6.L'], 'contains': ['24.DA', '24.DG', '24.DK', '24.HN', '24.LS', '24.OF'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [5339, -1, 5231, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bp1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BP', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890666
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.K', '6.O'], 'contains': ['24.DB', '24.DC', '24.DD', '24.DW', '24.DX', '24.EV', '24.EW', '24.FF', '24.FG', '24.LO', '24.LT', '24.MO', '24.MR'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': [7680, -1, 7827, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.12.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bq1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BQ', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890667
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.A', '2.D', '2.E'], 'contains': ['8.A', '8.B', '8.D', '8.J', '12.CA', '16.I', '16.K'], 'core': '4.B', 'coset_action_label': None, 'count': 1, 'diagramx': [2228, 9365, 851, 9093], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 51090957482037557056, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.4.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': ['2.A', '2.D', '2.E'], 'normal_contains': ['8.A', '8.B', '8.D', '8.J'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.B', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890668
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.E', '6.H', '6.O'], 'contains': ['24.DB', '24.DE', '24.DJ', '24.HH', '24.LU', '24.OI'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6038, -1, 6274, -1], 'generators': [54003503616859417437382, 108169256199550431553913, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108118542983424833692672], 'label': '6144.ze.12.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.br1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BR', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890669
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.E', '6.K', '6.L'], 'contains': ['24.DB', '24.DG', '24.DI', '24.HO', '24.LV', '24.OG'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5557, -1, 5299, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 108118542993128400914047, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bs1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BS', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890670
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.K', '6.N'], 'contains': ['24.DC', '24.DH', '24.DI', '24.HZ', '24.LW', '24.OS'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5972, -1, 6444, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.12.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bt1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BT', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890671
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.J', '6.O'], 'contains': ['24.DC', '24.DJ', '24.DK', '24.IA', '24.LX', '24.OR'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5991, -1, 5827, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 51090961780558017359, 108118542983424833692672, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bu1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BU', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890672
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.I', '6.O'], 'contains': ['24.DD', '24.DE', '24.DK', '24.LY'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5630, -1, 5708, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108169256199550431553913, 377740048764960017], 'label': '6144.ze.12.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bv1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BV', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890673
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.K', '6.M'], 'contains': ['24.DD', '24.DG', '24.DH', '24.LZ'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5749, -1, 5870, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.12.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bw1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BW', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890674
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.E', '6.I', '6.N'], 'contains': ['24.DE', '24.DF', '24.DI', '24.MA'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5722, -1, 5733, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108118542993128400914047, 54003503616859417437382, 4097467157062, 51468697530548501041, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bx1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BX', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890675
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.E', '6.J', '6.M'], 'contains': ['24.DF', '24.DG', '24.DJ', '24.MB'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5774, -1, 5805, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 108118542983424833692672, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.by1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BY', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890676
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.DP', '24.DQ', '24.DR', '24.DT', '24.DU', '24.DW', '24.DY', '24.EX', '24.EY', '24.EZ', '24.FA', '24.FB', '24.FC', '24.FE', '24.FH', '24.LP', '24.MP'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7747, -1, 9144, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503622465652187519, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.12.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.bz1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BZ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890677
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B', '6.F', '6.L', '6.M'], 'contains': ['24.B', '24.CV', '24.DG', '24.DZ', '24.EC', '24.GZ', '24.HP', '24.HT', '24.KY', '24.MC', '24.ME', '24.NW', '24.OJ', '24.OL'], 'core': '24.B', 'coset_action_label': None, 'count': 3, 'diagramx': [2789, -1, 2294, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.ca1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CA', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890706
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.H', '6.P', '6.Q'], 'contains': ['24.KJ', '24.KN', '24.KO', '24.LC', '24.LE', '24.LR', '24.LU', '24.PJ', '24.PM'], 'core': '96.C', 'coset_action_label': None, 'count': 24, 'diagramx': [5700, -1, 5754, -1], 'generators': [54003503616859417437382, 108169256199550431553913, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165248982343715247, 108118542983424833692672], 'label': '6144.ze.12.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.da1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DA', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890678
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.W', '1536.Y', '1536.X'], 'conjugacy_class_count': 1, 'contained_in': ['2.B', '2.D', '2.F'], 'contains': ['8.A', '8.E', '8.U', '8.Z', '12.B', '16.N'], 'core': '4.C', 'coset_action_label': None, 'count': 1, 'diagramx': [674, 5126, 669, 1689], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 377748450845332417, 1313941673647, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.4.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': ['2.B', '2.D', '2.F'], 'normal_contains': ['8.A', '8.E', '12.B'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '2500.l', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.C', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890679
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.D', '6.G', '6.L', '6.O'], 'contains': ['24.B', '24.DB', '24.DK', '24.DL', '24.DO', '24.HG', '24.HL', '24.HV', '24.LG', '24.LJ', '24.MF', '24.OC', '24.OE', '24.ON'], 'core': '24.B', 'coset_action_label': None, 'count': 3, 'diagramx': [891, -1, 1809, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 51468700347165007319, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.12.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cb1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CB', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890680
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.E', '6.F', '6.N', '6.O'], 'contains': ['24.B', '24.DC', '24.DE', '24.EA', '24.EB', '24.HM', '24.HR', '24.HW', '24.LK', '24.MD', '24.MG', '24.OD', '24.OK', '24.OO'], 'core': '24.B', 'coset_action_label': None, 'count': 3, 'diagramx': [2940, -1, 3150, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.12.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cc1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CC', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890681
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.G', '6.G', '6.M', '6.N'], 'contains': ['24.B', '24.DF', '24.DH', '24.DM', '24.DN', '24.LH', '24.LM', '24.MH'], 'core': '24.B', 'coset_action_label': None, 'count': 3, 'diagramx': [2021, -1, 2346, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.12.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cd1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CD', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890682
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.F'], 'contains': ['24.FJ', '24.FK', '24.FM', '24.FN', '24.FP', '24.FQ', '24.FR', '24.GV', '24.GX', '24.HC', '24.HI', '24.HP', '24.HQ', '24.HR', '24.HS', '24.OT', '24.OU', '24.OV', '24.OW'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4258, -1, 4064, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503618341535830447, 53952412685900568952456, 54003503622465652187519, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.12.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.ce1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CE', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890683
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.F'], 'contains': ['24.FJ', '24.FL', '24.FM', '24.FO', '24.FW', '24.FX', '24.FZ', '24.GG', '24.GH', '24.GI', '24.GJ', '24.GV', '24.GZ', '24.HC', '24.HM', '24.OY', '24.OZ', '24.PA', '24.PB'], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [3396, -1, 3857, -1], 'generators': [108169256206464380536342, 51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 108118165246159714329599, 1313941673647, 54003503616859417437382], 'label': '6144.ze.12.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.cf1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CF', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890684
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.P', '6.F'], 'contains': ['24.FL', '24.FO', '24.FP', '24.FR', '24.GA', '24.GB', '24.GC', '24.GH', '24.GJ', '24.GK', '24.GL', '24.HQ', '24.HS', '24.HT', '24.HW', '24.OX', '24.PC', '24.PD', '24.PE'], 'core': '48.D', 'coset_action_label': None, 'count': 12, 'diagramx': [3352, -1, 3342, -1], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 51090954698471793966, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.12.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.cg1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CG', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890685
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.F'], 'contains': ['24.FK', '24.FN', '24.FW', '24.FX', '24.GA', '24.GB', '24.GE', '24.GG', '24.GI', '24.GK', '24.GL', '24.GQ', '24.GT', '24.HP', '24.HR', '24.PF', '24.PG', '24.PH', '24.PI'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4226, -1, 3652, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503618341535830447, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.ch1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CH', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890686
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.H'], 'contains': ['24.GQ', '24.GR', '24.GS', '24.GW', '24.GY', '24.HE', '24.HH', '24.PJ'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6829, -1, 6380, -1], 'generators': [51090957482037557056, 108118165250283830616367, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.12.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '12.ci1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CI', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890687
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.H'], 'contains': ['24.GW', '24.GX', '24.GY', '24.HD', '24.HE', '24.HF', '24.HH', '24.PM'], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6892, -1, 6425, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503618341535830447, 53952412685900568952456, 108118542983424833692672, 51091303471599669696, 187922473373129593564937, 122003583856732942], 'label': '6144.ze.12.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '12.cj1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CJ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890688
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.L'], 'contains': ['24.GZ', '24.HA', '24.HB', '24.HK', '24.HL', '24.HN', '24.HO', '24.PL', '24.PN'], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [962, -1, 1253, -1], 'generators': [1313941668480, 108118165246159714329599, 25903229683158464676480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.ck1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CK', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890689
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.W', '1536.Y', '1536.X'], 'conjugacy_class_count': 1, 'contained_in': ['2.C', '2.D', '2.G'], 'contains': ['8.A', '8.F', '8.V', '8.BA', '12.CB', '16.L', '16.O'], 'core': '4.D', 'coset_action_label': None, 'count': 1, 'diagramx': [330, 3773, 583, 6503], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 51468700347165007319, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.4.D', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': ['2.C', '2.D', '2.G'], 'normal_contains': ['8.A', '8.F'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '2500.l', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.D', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890690
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.Q', '6.L'], 'contains': ['24.HA', '24.HB', '24.HN', '24.HO', '24.HT', '24.HU', '24.HV', '24.PK', '24.PO'], 'core': '48.D', 'coset_action_label': None, 'count': 12, 'diagramx': [870, -1, 1137, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.cl1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CL', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890691
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.B'], 'contains': ['24.ID', '24.IE', '24.IG', '24.IH', '24.IM', '24.JO', '24.JP', '24.JS', '24.JU', '24.KA', '24.KB', '24.KE', '24.KG', '24.KZ', '24.LA', '24.LB', '24.LN', '24.LO', '24.LP'], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [9040, -1, 7959, -1], 'generators': [51090957482037557056, 4097467157062, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 377740048764960017, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.12.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.cm1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CM', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890692
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.B', '6.P', '6.Q'], 'contains': ['24.IE', '24.IF', '24.IM', '24.IN', '24.IO', '24.JQ', '24.JR', '24.JT', '24.JV', '24.KC', '24.KD', '24.KF', '24.KH', '24.LB', '24.LC', '24.LD', '24.LP', '24.LQ', '24.LT'], 'core': '48.E', 'coset_action_label': None, 'count': 24, 'diagramx': [7631, -1, 7415, -1], 'generators': [5606234750137, 25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.12.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cn1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CN', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890693
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.C', '6.P', '6.Q'], 'contains': ['24.IF', '24.IQ', '24.IR', '24.LE', '24.LF', '24.LW', '24.LX'], 'core': '96.B', 'coset_action_label': None, 'count': 24, 'diagramx': [5212, -1, 5597, -1], 'generators': [5606234750137, 54003503616859417437382, 51090961780558017359, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118542983424833692672], 'label': '6144.ze.12.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.co1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CO', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890694
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.D', '6.P', '6.Q'], 'contains': ['24.IN', '24.IP', '24.IQ', '24.LR', '24.LS', '24.LY', '24.LZ'], 'core': '48.E', 'coset_action_label': None, 'count': 24, 'diagramx': [5317, -1, 5429, -1], 'generators': [5606234750137, 54003503616859417437382, 108169256199550431553913, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 377740048764960017, 122003583856732942], 'label': '6144.ze.12.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cp1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CP', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890695
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.E', '6.P', '6.Q'], 'contains': ['24.IO', '24.IP', '24.IR', '24.LU', '24.LV', '24.MA', '24.MB'], 'core': '96.B', 'coset_action_label': None, 'count': 24, 'diagramx': [5471, -1, 5684, -1], 'generators': [5606234750137, 54003503616859417437382, 108169256199550431553913, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118542983424833692672], 'label': '6144.ze.12.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CQ', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890696
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.B'], 'contains': ['24.IS', '24.IT', '24.IY', '24.IZ', '24.JB', '24.JO', '24.JP', '24.JT', '24.JV', '24.KA', '24.KB', '24.KF', '24.KH', '24.MI', '24.MJ', '24.MK', '24.MN', '24.MO', '24.MP'], 'core': '48.E', 'coset_action_label': None, 'count': 24, 'diagramx': [9281, -1, 7937, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942, 51090957482037557056, 51091304773086570816], 'label': '6144.ze.12.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.cr1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CR', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890697
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.B'], 'contains': ['24.IT', '24.IU', '24.JB', '24.JC', '24.JD', '24.JQ', '24.JR', '24.JS', '24.JU', '24.KC', '24.KD', '24.KE', '24.KG', '24.MK', '24.ML', '24.MM', '24.MP', '24.MQ', '24.MR'], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [9166, -1, 7882, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503615545556328262, 4097467157062, 53952413034673736392198, 122003583856732942, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.12.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.cs1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CS', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890698
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.F', '6.P'], 'contains': ['24.IF', '24.IP', '24.JG', '24.JH', '24.JM', '24.JW', '24.JX', '24.KJ', '24.KP', '24.KY', '24.LK', '24.OT', '24.OX', '24.PA', '24.PF'], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [4527, -1, 4522, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 108118165244677595913462, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.ct1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CT', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890699
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.G'], 'contains': ['24.IK', '24.IL', '24.IW', '24.IX', '24.JD', '24.JE', '24.JL', '24.KL', '24.KM', '24.KS', '24.KT', '24.KW', '24.KX', '24.LG', '24.LH'], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1574, -1, 2378, -1], 'generators': [25903229683158464676480, 1313941673647, 4097467157062, 51468697530548501041, 53952413034673736392198, 122003583856732942, 108118165243376109012342, 51091304773086570816, 51091299166851820921], 'label': '6144.ze.12.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '12.cu1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CU', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229890700
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.BD'], 'conjugacy_class_count': 1, 'contained_in': ['2.A', '2.F', '2.G'], 'contains': ['8.A', '8.G', '8.W', '8.BB', '12.CC', '16.J', '16.P'], 'core': '4.E', 'coset_action_label': None, 'count': 1, 'diagramx': [2255, 7071, 877, 3621], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 242140587575261560029503, 4097467157062, 108118165243376109012342, 51090961780558017359, 54003503616859417437382], 'label': '6144.ze.4.E', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': ['2.A', '2.F', '2.G'], 'normal_contains': ['8.A', '8.G'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '2500.l', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.E', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890701
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.A', '6.P'], 'contains': ['24.IN', '24.IR', '24.IY', '24.JA', '24.JM', '24.KN', '24.KQ', '24.KU', '24.KV', '24.LI', '24.LL'], 'core': '48.E', 'coset_action_label': None, 'count': 12, 'diagramx': [5603, -1, 5778, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 108118542983424833692672, 54003503616859417437382, 4097467157062, 108118165244677595913462, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cv1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CV', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229890702
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.G', '6.P'], 'contains': ['24.IO', '24.IQ', '24.IW', '24.IX', '24.JM', '24.KO', '24.KR', '24.KS', '24.KT', '24.LJ', '24.LM'], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [2767, -1, 4482, -1], 'generators': [54003503616859417437382, 108118165250283830616367, 51468697530548501041, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.12.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cw1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CW', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890703
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.F'], 'contains': ['24.ID', '24.II', '24.JG', '24.JH', '24.JJ', '24.JK', '24.JN', '24.JW', '24.JX', '24.JY', '24.JZ', '24.KI', '24.KK', '24.MC', '24.MD', '24.OU', '24.OV', '24.OY', '24.OZ', '24.PC', '24.PD', '24.PG', '24.PH'], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [3573, -1, 4028, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503615545556328262, 54003503622465652187519, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.12.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.cx1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CX', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890704
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.H', '6.F', '6.Q'], 'contains': ['24.C', '24.IF', '24.IP', '24.JJ', '24.JK', '24.JY', '24.JZ', '24.KJ', '24.KP', '24.ME', '24.MG', '24.OW', '24.PB', '24.PE', '24.PI'], 'core': '24.C', 'coset_action_label': None, 'count': 12, 'diagramx': [3491, -1, 3557, -1], 'generators': [5606234750137, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cy1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CY', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890705
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.CZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.J', '6.G', '6.Q'], 'contains': ['24.C', '24.IK', '24.IL', '24.IO', '24.IQ', '24.KL', '24.KM', '24.KO', '24.KR', '24.MF', '24.MH'], 'core': '24.C', 'coset_action_label': None, 'count': 12, 'diagramx': [1970, -1, 2319, -1], 'generators': [5606234750137, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 51468700347165007319, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.12.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cz1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CZ', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890707
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.I', '6.P', '6.Q'], 'contains': ['24.KJ', '24.KQ', '24.KR', '24.LD', '24.LF', '24.LY', '24.MA'], 'core': '96.D', 'coset_action_label': None, 'count': 24, 'diagramx': [5082, -1, 5454, -1], 'generators': [54003503616859417437382, 108169256199550431553913, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 377740048764960017, 122003583856732942, 108118165248982343715247], 'label': '6144.ze.12.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.db1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DB', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890708
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.J', '6.P', '6.Q'], 'contains': ['24.KN', '24.KP', '24.KR', '24.LQ', '24.LS', '24.LX', '24.MB'], 'core': '96.C', 'coset_action_label': None, 'count': 24, 'diagramx': [5288, -1, 5567, -1], 'generators': [25903229683158464676480, 1313941673647, 51090961780558017359, 108118542983424833692672, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108118165248982343715247], 'label': '6144.ze.12.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.dc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DC', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890709
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.K', '6.P', '6.Q'], 'contains': ['24.KO', '24.KP', '24.KQ', '24.LT', '24.LV', '24.LW', '24.LZ'], 'core': '96.D', 'coset_action_label': None, 'count': 24, 'diagramx': [5401, -1, 5628, -1], 'generators': [25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108118165248982343715247, 377740048764960017], 'label': '6144.ze.12.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.dd1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DD', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890710
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.L', '6.P'], 'contains': ['24.KY', '24.LC', '24.LF', '24.LI', '24.LJ', '24.LS', '24.LV', '24.PK', '24.PL'], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [4878, -1, 4462, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.12.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.de1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DE', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890711
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.W', '1536.Y', '1536.X', '1536.BD'], 'conjugacy_class_count': 1, 'contained_in': ['2.B', '2.E', '2.G'], 'contains': ['8.A', '8.H', '12.C', '16.Q'], 'core': '4.F', 'coset_action_label': None, 'count': 1, 'diagramx': [801, 1855, 738, 2352], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 377740048764960017, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.4.F', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.F', 'normal_contained_in': ['2.B', '2.E', '2.G'], 'normal_contains': ['8.A', '8.H', '12.C'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '2500.l', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.F', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890712
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.M', '6.P'], 'contains': ['24.KY', '24.LD', '24.LE', '24.LL', '24.LM', '24.LZ', '24.MB'], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [5240, -1, 5510, -1], 'generators': [25903229683158464676480, 1313941673647, 108118542983424833692672, 54003503616859417437382, 4097467157062, 108118165244677595913462, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.df1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DF', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890713
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.N', '6.P'], 'contains': ['24.LI', '24.LK', '24.LM', '24.LQ', '24.LR', '24.LW', '24.MA'], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5181, -1, 5376, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 51468697530548501041, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.12.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.dg1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DG', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890714
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.O', '6.P'], 'contains': ['24.LJ', '24.LK', '24.LL', '24.LT', '24.LU', '24.LX', '24.LY'], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [5054, -1, 5482, -1], 'generators': [25903229683158464676480, 1313941673647, 51090961780558017359, 108118542983424833692672, 54003503616859417437382, 4097467157062, 108118165244677595913462, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.dh1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DH', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890715
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.K', '6.L', '6.Q'], 'contains': ['24.D', '24.LC', '24.LF', '24.LS', '24.LV', '24.ME', '24.MF', '24.PN', '24.PO'], 'core': '24.D', 'coset_action_label': None, 'count': 12, 'diagramx': [1996, -1, 2014, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056, 377749752252399937], 'label': '6144.ze.12.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.di1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DI', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890716
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.L', '6.M', '6.Q'], 'contains': ['24.E', '24.LD', '24.LE', '24.LZ', '24.MB', '24.ME', '24.MH'], 'core': '24.E', 'coset_action_label': None, 'count': 12, 'diagramx': [5109, -1, 5404, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.12.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.L', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.dj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DJ', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890717
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.M', '6.N', '6.Q'], 'contains': ['24.D', '24.LQ', '24.LR', '24.LW', '24.MA', '24.MG', '24.MH'], 'core': '24.D', 'coset_action_label': None, 'count': 12, 'diagramx': [4933, -1, 5274, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 51091303471599669696, 108118165243376109012342, 122003583856732942, 377749752252399937], 'label': '6144.ze.12.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.dk1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DK', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890718
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.N', '6.O', '6.Q'], 'contains': ['24.E', '24.LT', '24.LU', '24.LX', '24.LY', '24.MF', '24.MG'], 'core': '24.E', 'coset_action_label': None, 'count': 12, 'diagramx': [4903, -1, 5324, -1], 'generators': [25903229683158464676480, 1313941673647, 51090963094498960079, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342, 377740048764960017], 'label': '6144.ze.12.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.N', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.dl1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DL', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890719
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.F'], 'contains': ['24.MS', '24.MU', '24.MZ', '24.NA', '24.NE', '24.NI', '24.NJ', '24.NM', '24.NP', '24.NW', '24.OD', '24.OU', '24.OX', '24.PB', '24.PG'], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [3710, -1, 4006, -1], 'generators': [6920176418617, 108118165246159714329599, 25903229683158464676480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 108118165244677595913462, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.dm1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DM', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890720
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.F'], 'contains': ['24.MT', '24.MV', '24.MZ', '24.NA', '24.NC', '24.ND', '24.NG', '24.NI', '24.NJ', '24.NK', '24.NL', '24.NN', '24.NS', '24.OJ', '24.OK', '24.OT', '24.OW', '24.OY', '24.OZ', '24.PC', '24.PD', '24.PF', '24.PI'], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [4003, -1, 3509, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503618341535830447, 53952412685900568952456, 54003503615545556328262, 54003503622465652187519, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.12.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.dn1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DN', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890721
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.R', '6.F'], 'contains': ['24.MS', '24.MU', '24.NC', '24.ND', '24.NH', '24.NK', '24.NL', '24.NM', '24.NP', '24.OL', '24.OO', '24.OV', '24.PA', '24.PE', '24.PH'], 'core': '48.G', 'coset_action_label': None, 'count': 12, 'diagramx': [3330, -1, 3385, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 2796059363782, 122003583856732942, 108118165243376109012342, 51090957482037557056], 'label': '6144.ze.12.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.do1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DO', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890722
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.W', '1536.X', '1536.Y', '1536.BD'], 'conjugacy_class_count': 1, 'contained_in': ['2.C', '2.E', '2.F'], 'contains': ['8.A', '8.I', '12.CD', '16.M', '16.R'], 'core': '4.G', 'coset_action_label': None, 'count': 1, 'diagramx': [603, 7810, 827, 7698], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382, 51468697530548501041], 'label': '6144.ze.4.G', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': ['2.C', '2.E', '2.F'], 'normal_contains': ['8.A', '8.I'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '2500.l', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.G', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890723
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.H'], 'contains': ['24.NN', '24.NQ', '24.NR', '24.NZ', '24.OA', '24.OH', '24.OI', '24.PJ', '24.PM'], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [6397, -1, 6585, -1], 'generators': [53952412685900568952456, 187922473373129593564937, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.12.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '12.dp1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DP', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890724
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.L'], 'contains': ['24.NW', '24.NX', '24.NY', '24.OB', '24.OC', '24.OF', '24.OG', '24.PK', '24.PN'], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [911, -1, 1356, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941673647, 108169256206464380536342, 54003503616859417437382, 108118165244677595913462, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.dq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DQ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890725
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.DR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.S', '6.L'], 'contains': ['24.NX', '24.NY', '24.OF', '24.OG', '24.OL', '24.OM', '24.ON', '24.PL', '24.PO'], 'core': '48.G', 'coset_action_label': None, 'count': 12, 'diagramx': [846, -1, 1156, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 377748450845332417, 51091303471599669696, 2796059363782, 122003583856732942, 108118165243376109012342, 51090957482037557056], 'label': '6144.ze.12.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.dr1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DR', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890726
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['384.F', '384.G', '384.E', '384.D'], 'conjugacy_class_count': 1, 'contained_in': ['8.A', '8.B', '8.T', '8.U', '8.V', '8.W'], 'contains': ['32.A', '48.D'], 'core': '16.A', 'coset_action_label': None, 'count': 1, 'diagramx': [718, 6238, 710, 5212], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 242140587575261560029503, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.16.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '16.A', 'normal_contained_in': ['8.A', '8.B'], 'normal_contains': ['32.A', '48.D'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '2500.l', 'quotient_action_image': '16.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.A', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890727
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.A', '8.C', '8.D', '8.E', '8.F', '8.G', '8.H', '8.I'], 'contains': ['32.A', '48.F'], 'core': '16.B', 'coset_action_label': None, 'count': 1, 'diagramx': [666, 4899, 662, 4153], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.16.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '16.B', 'normal_contained_in': ['8.A', '8.C', '8.D', '8.E', '8.F', '8.G', '8.H', '8.I'], 'normal_contains': ['32.A', '48.F'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.B', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890728
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['384.D', '384.E', '384.F', '384.G'], 'conjugacy_class_count': 1, 'contained_in': ['8.A', '8.J', '8.Y', '8.Z', '8.BA', '8.BB'], 'contains': ['32.A', '48.G'], 'core': '16.C', 'coset_action_label': None, 'count': 1, 'diagramx': [699, 5649, 686, 4683], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 2796059363782, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.16.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '16.C', 'normal_contained_in': ['8.A', '8.J'], 'normal_contains': ['32.A', '48.G'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '6144.ze', 'quotient_action_image': '16.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.C', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890729
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['384.H', '384.I', '384.J', '384.K', '384.L', '384.M', '384.N', '384.O', '384.P', '384.Q', '384.R', '384.G', '384.F', '384.D', '384.E', '384.S', '384.T', '384.U', '384.V', '384.W', '384.X', '384.Y', '384.Z', '384.BA', '384.BB', '384.BC', '384.BD', '384.BE'], 'conjugacy_class_count': 4, 'contained_in': ['8.B', '8.D', '8.J', '8.BC', '8.BD'], 'contains': ['32.A'], 'core': '16.D', 'coset_action_label': None, 'count': 4, 'diagramx': [754, 7467, 727, 7340], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090953384530851246], 'label': '6144.ze.16.D', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '16.D', 'normal_contained_in': ['8.B', '8.D', '8.J'], 'normal_contains': ['32.A'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': '6144.ze', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.D', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890730
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '8.K'], 'contains': ['32.E', '32.L', '32.M', '32.W', '32.BK'], 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2294, -1, 1497, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 242140587575261560029503, 6920176418617, 1313941673647, 51091303471599669696, 108118165243376109012342], 'label': '6144.ze.16.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '16.e1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.E', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229890731
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.O'], 'contains': ['32.B', '32.C', '32.D', '32.F', '32.G', '32.I', '32.J', '32.X', '64.B'], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [2130, -1, 101, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 242140587575261560029503, 1313941673647, 51090957482037557056, 377740048764960017, 51091299166851820921], 'label': '6144.ze.16.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '16.f1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.F', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 229890732
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '8.M'], 'contains': ['32.H', '32.O', '32.Z', '32.BL'], 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': [290, -1, 894, -1], 'generators': [122000787877207687, 187973563958306240457616, 108118287248261452641239, 51091299166851820921, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.16.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.M', 'old_label': '16.g1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.G', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 229890733
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.BI', '1536.BJ', '1536.BK', '1536.BL', '1536.BD', '1536.BG', '1536.BF', '1536.BE', '1536.BH'], 'conjugacy_class_count': 4, 'contained_in': ['2.A', '2.H'], 'contains': ['8.C', '8.D', '8.G', '8.BC', '12.CY', '16.W', '16.X'], 'core': '4.H', 'coset_action_label': None, 'count': 4, 'diagramx': [1837, 6396, 899, 5289], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941673647, 5606234750137, 51090957482037557056, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.4.H', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.H', 'normal_contained_in': ['2.A', '2.H'], 'normal_contains': ['8.C', '8.D', '8.G'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '6144.ze', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.H', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890734
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '8.L', '8.N', '8.O'], 'contains': ['32.K', '32.N', '32.Y', '32.BM', '48.A'], 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1820, -1, 542, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51091299166851820921], 'label': '6144.ze.16.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.h1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.H', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890735
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B', '8.K'], 'contains': ['32.E', '32.P', '32.BA', '32.BN'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2230, -1, 1391, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 242140587575261560029503, 1313941673647, 51091303471599669696, 108118165243376109012342, 51090957482037557056], 'label': '6144.ze.16.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '16.i1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.I', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229890736
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.E', '8.K'], 'contains': ['32.E', '32.Q', '32.BB', '32.BO'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2208, -1, 1439, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 242140587575261560029503, 1313941673647, 51090961780558017359, 51091303471599669696, 108118165243376109012342], 'label': '6144.ze.16.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '16.j1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.J', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229890739
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.G', '8.M'], 'contains': ['32.H', '32.BE'], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': [143, -1, 804, -1], 'generators': [122000787877207687, 187973563958306240457616, 51468697530548501041, 108118287248261452641239, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.16.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.M', 'old_label': '16.m1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.M', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 229890740
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.C', '8.N', '8.P', '8.R'], 'contains': ['32.K', '32.S', '32.BF', '32.BR', '48.B'], 'core': '48.B', 'coset_action_label': None, 'count': 4, 'diagramx': [262, -1, 237, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 4097467157062, 122003583856732942], 'label': '6144.ze.16.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.n1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.N', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890741
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.D', '8.O', '8.P', '8.S'], 'contains': ['32.K', '32.T', '32.BG', '32.BS'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': [230, -1, 140, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 242089496283014884627199, 51468700347165007319, 122003583856732942], 'label': '6144.ze.16.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.o1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.O', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890742
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.E', '8.L', '8.R', '8.S'], 'contains': ['32.K', '32.V', '32.BH', '32.BT'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1767, -1, 488, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 242089496283014884627199, 122003583856732942], 'label': '6144.ze.16.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.p1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.P', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890743
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.F', '8.N', '8.Q', '8.S'], 'contains': ['32.K', '32.BI', '48.C'], 'core': '48.C', 'coset_action_label': None, 'count': 4, 'diagramx': [535, -1, 307, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 377740048764960017], 'label': '6144.ze.16.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.q1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.Q', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229890744
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.BB', '1536.BA', '1536.Z', '1536.W', '1536.Y', '1536.X', '1536.BC', '1536.BD', '1536.B', '1536.D', '1536.E', '1536.C', '1536.BG', '1536.BF', '1536.BE', '1536.BH'], 'conjugacy_class_count': 4, 'contained_in': ['2.B', '2.H'], 'contains': ['8.C', '8.E', '8.H', '12.D', '16.Y'], 'core': '4.I', 'coset_action_label': None, 'count': 4, 'diagramx': [736, 371, 712, 1019], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942, 377741362626794897], 'label': '6144.ze.4.I', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.I', 'normal_contained_in': ['2.B', '2.H'], 'normal_contains': ['8.C', '8.E', '8.H', '12.D'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': '6144.ze', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.I', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890745
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.G', '8.O', '8.Q', '8.R'], 'contains': ['32.K', '32.BJ'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': [478, -1, 401, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 122003583856732942], 'label': '6144.ze.16.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.r1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.R', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229890746
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.P', '8.K'], 'contains': ['32.L', '32.P', '32.Q', '32.BU', '64.A'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': [2525, -1, 1519, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 51091303471599669696, 108118165243376109012342, 216237479891421308907006, 51090954698471793966], 'label': '6144.ze.16.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '16.s1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.S', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229890747
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.P', '8.K'], 'contains': ['32.M', '32.P', '32.Q', '32.BV'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': [2547, -1, 1541, -1], 'generators': [187922473367523358862032, 51212595668145448193, 122010491578389112, 51090954698471793966, 25903229683158464676480, 1313941673647, 1313941668480, 216237479891421308907006], 'label': '6144.ze.16.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '16.t1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.T', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229890748
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.P', '8.L'], 'contains': ['32.N', '32.R', '32.V', '32.BW'], 'core': '192.H', 'coset_action_label': None, 'count': 16, 'diagramx': [2347, -1, 863, -1], 'generators': [25903229683158464676480, 51091299166851820921, 122003583856732942, 1313941668480, 1313941673647, 51090954698471793966, 242140587575261560029503, 54003503616859417437382], 'label': '6144.ze.16.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.L', 'old_label': '16.u1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.U', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229890749
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.Q', '8.P'], 'contains': ['32.R', '32.S', '32.T', '32.BX'], 'core': '192.H', 'coset_action_label': None, 'count': 16, 'diagramx': [203, -1, 193, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 122003583856732942, 51090957482037557056], 'label': '6144.ze.16.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.P', 'old_label': '16.v1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.V', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229890750
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.H', '8.K'], 'contains': ['32.W', '32.BA', '32.BB', '32.BU', '32.BV'], 'core': '384.B', 'coset_action_label': None, 'count': 32, 'diagramx': [2180, -1, 1418, -1], 'generators': [122000787877207687, 25903229683158464676480, 242140587575261560029503, 5606234750137, 1313941673647, 51090961780558017359, 51091303471599669696, 108118165243376109012342], 'label': '6144.ze.16.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '16.w1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.W', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229890751
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.H', '8.L', '8.X'], 'contains': ['32.Y', '32.BC', '32.BH', '32.BW'], 'core': '96.B', 'coset_action_label': None, 'count': 16, 'diagramx': [592, -1, 520, -1], 'generators': [25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 242089496283014884627199, 51091297865364919801, 122003583856732942], 'label': '6144.ze.16.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.x1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.X', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890752
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.I', '8.N', '8.X'], 'contains': ['32.Y', '32.BF', '32.BI', '48.E'], 'core': '48.E', 'coset_action_label': None, 'count': 16, 'diagramx': [415, -1, 279, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 377740048764960017, 51091299166851820921], 'label': '6144.ze.16.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.y1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.Y', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890753
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.J', '8.O', '8.X'], 'contains': ['32.Y', '32.BG', '32.BJ'], 'core': '96.B', 'coset_action_label': None, 'count': 16, 'diagramx': [343, -1, 376, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51468696229140707761, 51091299166851820921], 'label': '6144.ze.16.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.z1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.Z', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890754
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.J', '8.M'], 'contains': ['32.Z', '32.BD', '32.BE'], 'core': '384.B', 'coset_action_label': None, 'count': 32, 'diagramx': [122, -1, 783, -1], 'generators': [122000787877207687, 187973563958306240457616, 51468697530548501041, 108118287248261452641239, 242140587575261560029503, 25903229683158464676480, 1313941673647, 51091297865364919801], 'label': '6144.ze.16.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.M', 'old_label': '16.ba1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BA', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 229890755
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '2.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['3072.B', '3072.H'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.A', '4.B', '4.E', '4.H', '4.P', '4.R', '6.F', '8.K', '8.L'], 'core': '2.A', 'coset_action_label': None, 'count': 1, 'diagramx': [2285, 6602, 910, 4990], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 51090957482037557056, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.2.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A', '4.B', '4.E', '4.H'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '2500.l', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.A', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891298
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['384.D', '384.E', '384.I', '384.T', '384.X', '384.BC'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 25903229681844523008000, 377741362626800062, 51091297865364924726], 'label': '6144.ze.192.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '192.a1.NC5', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.F', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229890756
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.BB', '1536.BA', '1536.Z', '1536.W', '1536.Y', '1536.X', '1536.BC', '1536.B', '1536.C', '1536.D', '1536.E', '1536.BD', '1536.BI', '1536.BJ', '1536.BK', '1536.BL'], 'conjugacy_class_count': 4, 'contained_in': ['2.C', '2.H'], 'contains': ['8.C', '8.F', '8.I', '12.CZ', '16.Z', '16.BA'], 'core': '4.J', 'coset_action_label': None, 'count': 4, 'diagramx': [499, 2548, 805, 7073], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941673647, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382, 51468697530548501041], 'label': '6144.ze.4.J', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.J', 'normal_contained_in': ['2.C', '2.H'], 'normal_contains': ['8.C', '8.F', '8.I'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '6144.ze', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.J', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890757
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.K', '8.P', '8.X'], 'contains': ['32.BC', '32.BF', '32.BG', '32.BX'], 'core': '96.C', 'coset_action_label': None, 'count': 16, 'diagramx': [311, -1, 215, -1], 'generators': [25903229683158464676480, 1313941673647, 51347039909644252801, 54003503616859417437382, 4097467157062, 242089496283014884627199, 51468700347165007319, 122003583856732942], 'label': '6144.ze.16.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.K', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.bb1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BB', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890758
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.L', '8.Q', '8.X'], 'contains': ['32.BC', '32.BI', '32.BJ'], 'core': '96.D', 'coset_action_label': None, 'count': 16, 'diagramx': [507, -1, 335, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.16.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.L', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.bc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BC', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229890759
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.M', '8.R', '8.X'], 'contains': ['32.BF', '32.BH', '32.BJ'], 'core': '96.C', 'coset_action_label': None, 'count': 16, 'diagramx': [443, -1, 357, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 4097467157062, 122003583856732942, 51468696229140707761], 'label': '6144.ze.16.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.M', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.bd1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BD', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890760
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.N', '8.S', '8.X'], 'contains': ['32.BG', '32.BH', '32.BI'], 'core': '96.D', 'coset_action_label': None, 'count': 16, 'diagramx': [392, -1, 257, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 242089496283014884627199, 51468700347165007319, 122003583856732942, 377741362626794897], 'label': '6144.ze.16.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '16.be1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BE', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890761
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.R', '8.K'], 'contains': ['32.BK', '32.BN', '32.BO', '32.BU', '32.BV'], 'core': '768.C', 'coset_action_label': None, 'count': 32, 'diagramx': [2483, -1, 1466, -1], 'generators': [187922473367523358862032, 51212595668145448193, 122010491578389112, 122002101738316807, 51090954698471793966, 25903229683158464676480, 1313941673647, 216237479891421308907006], 'label': '6144.ze.16.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '16.bf1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BF', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229890762
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.R', '8.L'], 'contains': ['32.BM', '32.BP', '32.BT', '32.BW'], 'core': '192.J', 'coset_action_label': None, 'count': 16, 'diagramx': [2267, -1, 831, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 2796059363782, 122003583856732942, 51090957482037557056, 51091299166851820921], 'label': '6144.ze.16.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.L', 'old_label': '16.bg1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BG', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229890763
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.S', '8.P'], 'contains': ['32.BP', '32.BR', '32.BS', '32.BX'], 'core': '192.J', 'coset_action_label': None, 'count': 16, 'diagramx': [176, -1, 167, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 2796059363782, 122003583856732942, 51090957482037557056], 'label': '6144.ze.16.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.P', 'old_label': '16.bh1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BH', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229890764
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.C', '8.T', '8.Y', '8.BC'], 'contains': ['32.A'], 'core': '32.A', 'coset_action_label': None, 'count': 4, 'diagramx': [737, -1, 759, -1], 'generators': [6920176418617, 25903229683158464676480, 242140587575261560029503, 1313941673647, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.16.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '16.bi1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BI', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 229890765
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.E', '8.U', '8.Z', '8.BD'], 'contains': ['32.A'], 'core': '32.A', 'coset_action_label': None, 'count': 4, 'diagramx': [627, -1, 643, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.16.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '16.bj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BJ', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 229890766
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.F', '8.V', '8.BA', '8.BD'], 'contains': ['32.A'], 'core': '32.A', 'coset_action_label': None, 'count': 4, 'diagramx': [376, -1, 622, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 51468700347165007319, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.16.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '16.bk1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BK', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 229890767
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.K', '1536.L', '1536.F', '1536.G', '1536.I', '1536.H', '1536.J', '1536.N', '1536.M', '1536.O', '1536.P', '1536.R', '1536.Q', '1536.U', '1536.V', '1536.T', '1536.S', '1536.W', '1536.Y', '1536.X', '1536.D', '1536.E', '1536.C', '1536.B'], 'conjugacy_class_count': 4, 'contained_in': ['2.D', '2.H'], 'contains': ['8.D', '8.E', '8.F', '8.BD', '12.DI', '16.BB'], 'core': '4.K', 'coset_action_label': None, 'count': 4, 'diagramx': [574, 4449, 648, 5896], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 51468700347165007319, 108118165243376109012342, 122003583856732942, 377749752252399937], 'label': '6144.ze.4.K', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.K', 'normal_contained_in': ['2.D', '2.H'], 'normal_contains': ['8.D', '8.E', '8.F'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': '6144.ze', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.K', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890768
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '16.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.G', '8.W', '8.BB', '8.BC'], 'contains': ['32.A'], 'core': '32.A', 'coset_action_label': None, 'count': 4, 'diagramx': [769, -1, 742, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 51090963094498960079, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.16.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '16.bl1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.BL', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 229890769
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': ['256.A', '256.B'], 'conjugacy_class_count': 1, 'contained_in': ['8.N', '12.G', '12.S'], 'contains': ['48.A', '48.B', '48.C', '48.E'], 'core': '24.A', 'coset_action_label': None, 'count': 1, 'diagramx': [7018, 6729, 6979, 7795], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 377740048764960017, 51091299166851820921], 'label': '6144.ze.24.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': ['6.A'], 'normal_contains': ['48.A', '48.B', '48.C', '48.E'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '2500.l', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.A', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 229890770
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.A', '12.A', '12.B', '12.C', '12.CA', '12.CB', '12.CC', '12.CD'], 'contains': ['48.D', '48.F', '48.G'], 'core': '24.B', 'coset_action_label': None, 'count': 1, 'diagramx': [1955, 4251, 1838, 2881], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': ['8.A', '12.A', '12.B', '12.C'], 'normal_contains': ['48.D', '48.F', '48.G', '96.A'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.B', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229890771
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['256.C', '256.D'], 'conjugacy_class_count': 2, 'contained_in': ['8.C', '12.A', '12.D', '12.CY', '12.CZ'], 'contains': ['48.F'], 'core': '24.C', 'coset_action_label': None, 'count': 2, 'diagramx': [1973, 2152, 2386, 2385], 'generators': [5606234750137, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '24.C', 'normal_contained_in': ['8.C', '12.A', '12.D'], 'normal_contains': ['48.F', '96.B'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '6144.ze', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.C', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229890772
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['256.E', '256.F'], 'conjugacy_class_count': 2, 'contained_in': ['8.E', '12.B', '12.D', '12.DI', '12.DK'], 'contains': ['48.F'], 'core': '24.D', 'coset_action_label': None, 'count': 2, 'diagramx': [1858, 3698, 1903, 1234], 'generators': [54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942, 377749752252399937], 'label': '6144.ze.24.D', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '24.D', 'normal_contained_in': ['8.E', '12.B', '12.D'], 'normal_contains': ['48.F', '96.C'], 'normalizer': '1.a1', 'old_label': '24.d1', 'projective_image': '6144.ze', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.D', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229890773
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['256.E', '256.F', '256.C', '256.D'], 'conjugacy_class_count': 2, 'contained_in': ['8.H', '12.C', '12.D', '12.DJ', '12.DL'], 'contains': ['48.F'], 'core': '24.E', 'coset_action_label': None, 'count': 2, 'diagramx': [2089, 3129, 4542, 1808], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.E', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '24.E', 'normal_contained_in': ['8.H', '12.C', '12.D'], 'normal_contains': ['48.F', '96.D'], 'normalizer': '1.a1', 'old_label': '24.e1', 'projective_image': '6144.ze', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.E', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229890774
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.F'], 'contains': [], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': [8459, -1, 9972, -1], 'generators': [25903229681844523008000, 6920176418617, 1313941673647, 25903364133006332138897, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '24.f1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.F', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890775
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.F'], 'contains': [], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': [8401, -1, 9916, -1], 'generators': [25903229687450757758137, 51090957482037557056, 25903229681844523008000, 4097467157062, 51091303471599669696, 1313941673647, 377740048764960017, 122003583856732942], 'label': '6144.ze.24.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '24.g1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.G', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229890776
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.F'], 'contains': [], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': [8440, -1, 9954, -1], 'generators': [25903229687450757758137, 25852138754983141680143, 25903229681844523008000, 4097467157062, 51091303471599669696, 1313941673647, 377740048764960017, 122003583856732942], 'label': '6144.ze.24.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '24.h1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.H', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229890777
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.F'], 'contains': [], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': [8479, -1, 9991, -1], 'generators': [25903229681844523008000, 6920176418617, 1313941673647, 25903364133006332138897, 4097467157062, 51091303471599669696, 25852138754983141680143, 122003583856732942], 'label': '6144.ze.24.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '24.i1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.I', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890778
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.K', '1536.F', '1536.G', '1536.I', '1536.H', '1536.J', '1536.L', '1536.BI', '1536.BJ', '1536.BK', '1536.BL', '1536.N', '1536.M', '1536.O', '1536.R', '1536.Q', '1536.P', '1536.S', '1536.T', '1536.U', '1536.V', '1536.W', '1536.Y', '1536.X', '1536.BD', '1536.D', '1536.E', '1536.C', '1536.B', '1536.BH', '1536.BG', '1536.BF', '1536.BE'], 'conjugacy_class_count': 4, 'contained_in': ['2.E', '2.H'], 'contains': ['8.D', '8.H', '8.I', '12.DJ', '16.BC'], 'core': '4.L', 'coset_action_label': None, 'count': 4, 'diagramx': [768, 8617, 764, 8424], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.4.L', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.L', 'normal_contained_in': ['2.E', '2.H'], 'normal_contains': ['8.D', '8.H', '8.I'], 'normalizer': '1.a1', 'old_label': '4.l1', 'projective_image': '6144.ze', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.L', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890779
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.W'], 'contains': [], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': [9033, -1, 8165, -1], 'generators': [25903229687450757758137, 25903229681844523008000, 1313941673647, 4097467157062, 25903107685154192786062, 53952413034673736392198, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.24.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '24.j1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.J', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890780
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.W'], 'contains': [], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': [9013, -1, 8146, -1], 'generators': [25903229681844523008000, 6920176418617, 1313941673647, 79804051672210232750640, 4097467157062, 25903107685154192786062, 53952413034673736392198, 51090957482037557056], 'label': '6144.ze.24.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '24.k1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.K', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890781
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.W'], 'contains': [], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': [8994, -1, 8127, -1], 'generators': [25903229681844523008000, 6920176418617, 1313941673647, 79804051672210232750640, 4097467157062, 25903107685154192786062, 25852138754983141680143, 53952413034673736392198], 'label': '6144.ze.24.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '24.l1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.L', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890782
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.W'], 'contains': [], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': [9052, -1, 8184, -1], 'generators': [25903229687450757758137, 25903229681844523008000, 1313941673647, 4097467157062, 25903107685154192786062, 25852138754983141680143, 53952413034673736392198, 54003247877598743421360], 'label': '6144.ze.24.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '24.m1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.M', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890783
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4714, -1, 4895, -1], 'generators': [122000787877207687, 51090957482037557056, 6920176418617, 108118287248261452641239, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.n1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.N', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890784
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.F', '12.O'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6752, -1, 7150, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.o1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.O', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890785
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1803, -1, 1756, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 53952291036669465204456, 1313941673647, 51468697530548501041, 108118165243376109012342, 51091299166851820921], 'label': '6144.ze.24.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.p1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.P', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890786
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.E', '12.G', '12.H', '12.I', '12.J', '12.K'], 'contains': ['48.A'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6020, -1, 6229, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.q1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Q', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229890787
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.L', '12.M'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1485, -1, 2173, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 53952413034673736392198, 122003583856732942, 108118165243376109012342, 51091299166851820921], 'label': '6144.ze.24.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.r1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.R', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 229890788
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.G', '12.N'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7931, -1, 9866, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.s1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.S', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890807
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.Q', '12.S'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8693, -1, 9595, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 122003583856732942, 54003247877598743421360, 51091299166851820921], 'label': '6144.ze.24.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bj1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BJ', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890808
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.R', '12.S'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8515, -1, 8720, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 122003583856732942, 377740048764960017, 51091299166851820921], 'label': '6144.ze.24.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bk1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BK', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890789
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.F', '1536.G', '1536.H', '1536.I', '1536.J', '1536.K', '1536.L', '1536.M', '1536.N', '1536.O', '1536.P', '1536.Q', '1536.R', '1536.S', '1536.T', '1536.U', '1536.V', '1536.W', '1536.X', '1536.Y', '1536.Z', '1536.BA', '1536.BB', '1536.BC', '1536.BD', '1536.BE', '1536.BF', '1536.BG', '1536.BH'], 'conjugacy_class_count': 4, 'contained_in': ['2.F', '2.H'], 'contains': ['8.E', '8.G', '8.I', '12.DK', '16.BD'], 'core': '4.M', 'coset_action_label': None, 'count': 4, 'diagramx': [714, 5760, 786, 4720], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51468696229140707761], 'label': '6144.ze.4.M', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.M', 'normal_contained_in': ['2.F', '2.H'], 'normal_contains': ['8.E', '8.G', '8.I'], 'normalizer': '1.a1', 'old_label': '4.m1', 'projective_image': '6144.ze', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.M', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890790
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.H', '12.N'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7722, -1, 9822, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 51468697530548501041, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.t1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.T', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890791
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.O', '12.P'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4804, -1, 4948, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 108169256206464380536342, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.u1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.U', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890792
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.N', '12.P'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6770, -1, 7132, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.v1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.V', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890793
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.K', '12.O'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4677, -1, 2693, -1], 'generators': [122000787877207687, 51090957482037557056, 6920176418617, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.w1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.W', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229890794
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.O', '12.P'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3902, -1, 3102, -1], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 4097467157062, 108118165243376109012342], 'label': '6144.ze.24.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.x1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.X', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890795
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.Q', '12.R'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8940, -1, 8535, -1], 'generators': [51090957482037557056, 4097467157062, 53952413034673736392198, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.y1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Y', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890796
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.Q', '12.S'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8291, -1, 9618, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 122003583856732942, 51090957482037557056, 377740048764960017, 51091299166851820921], 'label': '6144.ze.24.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.z1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Z', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890797
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.R', '12.S'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8226, -1, 8740, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 122003583856732942, 51090957482037557056, 54003247877598743421360, 51091299166851820921], 'label': '6144.ze.24.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ba1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BA', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890798
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.Q', '12.T'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9990, -1, 9732, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 53952035294625185894256, 4097467157062, 122003583856732942, 51090957482037557056, 51091299166851820921], 'label': '6144.ze.24.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bb1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BB', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890799
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.R', '12.T'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8888, -1, 9229, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 51347042732487422033, 122003583856732942, 51090957482037557056, 51091299166851820921], 'label': '6144.ze.24.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bc1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BC', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890800
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['1536.F', '1536.G', '1536.K', '1536.L', '1536.I', '1536.H', '1536.J', '1536.BI', '1536.BJ', '1536.BK', '1536.BL', '1536.N', '1536.M', '1536.O', '1536.R', '1536.Q', '1536.P', '1536.T', '1536.S', '1536.U', '1536.V', '1536.W', '1536.X', '1536.Y', '1536.BD', '1536.BA', '1536.BB', '1536.Z', '1536.BC'], 'conjugacy_class_count': 4, 'contained_in': ['2.G', '2.H'], 'contains': ['8.F', '8.G', '8.H', '12.DL', '16.BE'], 'core': '4.N', 'coset_action_label': None, 'count': 4, 'diagramx': [694, 3138, 690, 4190], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 51090963094498960079, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342, 377740048764960017], 'label': '6144.ze.4.N', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '4.N', 'normal_contained_in': ['2.G', '2.H'], 'normal_contains': ['8.F', '8.G', '8.H'], 'normalizer': '1.a1', 'old_label': '4.n1', 'projective_image': '6144.ze', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.N', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890801
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.L', '12.E', '12.S', '12.T'], 'contains': ['48.A'], 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7351, -1, 7094, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 51091299166851820921], 'label': '6144.ze.24.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bd1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BD', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890802
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.Q', '12.R'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8808, -1, 8411, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 53952413034673736392198, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.be1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BE', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890803
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.L', '12.Q'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6714, -1, 7347, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 51468697530548501041, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bf1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BF', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890804
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.L', '12.M'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1598, -1, 2430, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 53952413034673736392198, 122003583856732942, 187973307875878553928360], 'label': '6144.ze.24.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.bg1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BG', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229890805
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.M', '12.R'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6599, -1, 7002, -1], 'generators': [53952156946639855382521, 4097467157062, 53952413034673736392198, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bh1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BH', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890806
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.M', '12.L'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [513, -1, 1069, -1], 'generators': [122000787877207687, 187973563958306240457616, 51468697530548501041, 108118287248261452641239, 51091299166851820921, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.bi1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890809
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.Q', '12.T'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9947, -1, 9641, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 51347042732487422033, 122003583856732942, 51091299166851820921], 'label': '6144.ze.24.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bl1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BL', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890810
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.R', '12.T'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8916, -1, 9202, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 53952035294625185894256, 4097467157062, 122003583856732942, 51091299166851820921], 'label': '6144.ze.24.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bm1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BM', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890811
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.L', '8.N', '8.O', '8.P', '8.Q', '8.R', '8.S', '8.X', '12.S', '16.F'], 'core': '24.A', 'coset_action_label': None, 'count': 4, 'diagramx': [639, -1, 379, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 377740048764960017, 51091299166851820921], 'label': '6144.ze.4.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '4.o1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.O', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229890812
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.O', '12.H', '12.S', '12.T'], 'contains': ['48.A'], 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7174, -1, 7295, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 122003583856732942, 51091299166851820921], 'label': '6144.ze.24.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bn1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BN', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890813
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.K', '12.T'], 'contains': ['48.A'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7099, -1, 7428, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942, 51091299166851820921], 'label': '6144.ze.24.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bo1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BO', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229890814
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4822, -1, 5128, -1], 'generators': [122000787877207687, 51090957482037557056, 122010491578389112, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.bp1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BP', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890815
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O', '12.U', '12.BA'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5204, -1, 5071, -1], 'generators': [51090957482037557056, 108118165250283830616367, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bq1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BQ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890816
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O', '12.V', '12.BD'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5047, -1, 5110, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 108118165250283830616367, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.br1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BR', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890817
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.V', '12.BA'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3973, -1, 4745, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 53952412685900568952456, 108118165250283830616367, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bs1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BS', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890818
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.U', '12.BD'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4481, -1, 3652, -1], 'generators': [108118165250283830616367, 4097467157062, 187973564326514163969982, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bt1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BT', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890819
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.U', '12.V'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2796, -1, 3473, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bu1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890820
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.W', '12.X'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7910, -1, 7927, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 53952413034673736392198, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bv1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BV', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890821
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.W', '12.Y'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8957, -1, 9689, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 51347042732487422033, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bw1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BW', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890822
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.A'], 'contains': ['8.B', '8.T', '8.W', '8.BC', '12.CG', '16.S', '16.T', '16.U'], 'core': '8.B', 'coset_action_label': None, 'count': 4, 'diagramx': [2328, -1, 1004, -1], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 51090954698471793966, 242140587575261560029503, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.4.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '4.p1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.P', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 229890823
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.X', '12.Y'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8355, -1, 9770, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 53952035294625185894256, 4097467157062, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bx1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BX', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890824
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.W', '12.Z'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8975, -1, 9844, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 122003583856732942, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.24.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.by1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BY', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890825
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.X', '12.Z'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8378, -1, 9893, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.24.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bz1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BZ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890826
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.Y', '12.Z'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9435, -1, 9475, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ca1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CA', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890827
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.W', '12.X'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7889, -1, 8285, -1], 'generators': [25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 377740048764960017, 53952413034673736392198, 4097467157062], 'label': '6144.ze.24.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cb1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CB', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890828
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.W', '12.BG'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6668, -1, 7024, -1], 'generators': [53952156946639855382521, 1313941668480, 25903229683158464676480, 6920176418617, 1313941673647, 4097467157062, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cc1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CC', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891320
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.F'], 'contains': ['768.R', '768.S'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 5167, 25903364133006332138897, 51091297865364924726], 'label': '6144.ze.384.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.I', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229890829
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.X', '12.BH'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6628, -1, 7324, -1], 'generators': [25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 53952413034673736392198, 4097467157062, 51468697530548501041], 'label': '6144.ze.24.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cd1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CD', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890830
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.BG', '12.BH'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1415, -1, 2807, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 108169633946512931760000, 4097467157062, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ce1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CE', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229890831
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L', '12.BC', '12.BG'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1550, -1, 2710, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108118165250283830616367, 4097467157062, 53952413034673736392198, 122003583856732942, 187973307875878553928360], 'label': '6144.ze.24.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.cf1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CF', 'subgroup_fusion': None, 'weyl_group': '128.1758'}
  • id: 229890832
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L', '12.BF', '12.BH'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1573, -1, 2269, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108118165250283830616367, 4097467157062, 51468697530548501041, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.cg1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890833
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.D'], 'contains': ['8.B', '8.U', '8.V', '8.BD', '12.CL', '16.V'], 'core': '8.B', 'coset_action_label': None, 'count': 4, 'diagramx': [552, -1, 626, -1], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 377748450845332417, 1313941673647, 51090954698471793966, 242140587575261560029503, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.4.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '4.q1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.Q', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 229890834
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.M', '12.BC', '12.BH'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1438, -1, 2496, -1], 'generators': [108118165250283830616367, 4097467157062, 53952413034673736392198, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.24.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ch1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CH', 'subgroup_fusion': None, 'weyl_group': '128.1758'}
  • id: 229890835
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.M', '12.BF', '12.BG'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1288, -1, 2783, -1], 'generators': [53952156946639855382521, 108118165250283830616367, 4097467157062, 53952413034673736392198, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ci1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890836
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1760, -1, 1731, -1], 'generators': [122000787877207687, 187973563958306240457616, 51468697530548501041, 108118287248261452641239, 25903229683158464676480, 1313941673647, 1313941668480, 51212591375852361623], 'label': '6144.ze.24.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.cj1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CJ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890837
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.W', '12.Y'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9137, -1, 9669, -1], 'generators': [25903229683158464676480, 6920176418617, 53952412685900568952456, 122003583856732942, 1313941668480, 1313941673647, 53952035294625185894256, 4097467157062], 'label': '6144.ze.24.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ck1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CK', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890838
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.X', '12.Y'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8640, -1, 9751, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 51347042732487422033, 122003583856732942], 'label': '6144.ze.24.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cl1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CL', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890839
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.Y', '12.BB'], 'contains': ['48.B'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [7150, -1, 7452, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942], 'label': '6144.ze.24.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cm1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CM', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229890840
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.W', '12.Z'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9163, -1, 9710, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cn1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CN', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890841
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.Y', '12.Z'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9260, -1, 9532, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 122003583856732942], 'label': '6144.ze.24.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.co1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CO', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890842
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.X', '12.Z'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8664, -1, 9794, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 122003583856732942, 54003247877598743421360], 'label': '6144.ze.24.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cp1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CP', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890843
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.Z', '12.BE'], 'contains': ['48.C'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': [7041, -1, 7399, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cq1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CQ', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 229890844
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.A'], 'contains': ['8.J', '8.Y', '8.BB', '8.BC', '12.DO', '16.BF', '16.BG'], 'core': '8.J', 'coset_action_label': None, 'count': 4, 'diagramx': [2306, -1, 956, -1], 'generators': [6920176418617, 242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 2796059363782, 122003583856732942, 108118165243376109012342, 51090957482037557056], 'label': '6144.ze.4.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '4.r1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.R', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 229890845
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.K', '12.BB', '12.BE'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6196, -1, 6309, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51347042732487422033, 122003583856732942], 'label': '6144.ze.24.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.cr1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CR', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229890846
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4786, -1, 5032, -1], 'generators': [122000787877207687, 51090957482037557056, 122010491578389112, 108118287248261452641239, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.cs1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CS', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229890847
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.BA', '12.BB', '12.BC', '12.BD', '12.BE', '12.BF'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5733, -1, 5471, -1], 'generators': [54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ct1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CT', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890848
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.BG', '12.BH'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1397, -1, 2346, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 53952413034673736392198, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.cu1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CU', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 229890849
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.BA', '12.BI', '12.BJ', '12.BK', '12.BL', '12.CA'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6090, -1, 6008, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cv1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CV', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890850
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.U', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6808, -1, 7041, -1], 'generators': [51090957482037557056, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cw1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CW', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890851
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.BI', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8496, -1, 8831, -1], 'generators': [51090957482037557056, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cx1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CX', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890852
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.BJ', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8249, -1, 8885, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.24.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cy1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CY', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890853
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.CZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1668, -1, 1664, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 53952291036669465204456, 1313941673647, 51212591375852361623, 51468697530548501041, 108118165243376109012342], 'label': '6144.ze.24.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.cz1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CZ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890854
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.B', '12.G', '12.BB', '12.BI', '12.BN', '12.BO', '12.BP'], 'contains': ['48.B'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [6537, -1, 6466, -1], 'generators': [54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.da1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DA', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229890855
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '4.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.D'], 'contains': ['8.J', '8.Z', '8.BA', '8.BD', '12.DR', '16.BH'], 'core': '8.J', 'coset_action_label': None, 'count': 4, 'diagramx': [524, -1, 604, -1], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 377748450845332417, 1313941673647, 51090957482037557056, 242140587575261560029503, 2796059363782, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.4.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '4.s1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.S', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 229890856
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.BC', '12.BI', '12.BQ', '12.BR', '12.BS', '12.CB'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6293, -1, 6578, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 51468700347165007319, 122003583856732942], 'label': '6144.ze.24.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.db1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DB', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890857
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.BD', '12.BN', '12.BQ', '12.BT', '12.BU', '12.CC'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6312, -1, 6559, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dc1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DC', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890858
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.C', '12.G', '12.BE', '12.BJ', '12.BQ', '12.BV', '12.BW'], 'contains': ['48.C'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': [6116, -1, 6604, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dd1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DD', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890859
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.BA', '12.BO', '12.BR', '12.BV', '12.BX', '12.CC'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5755, -1, 5694, -1], 'generators': [54003503616859417437382, 108169256199550431553913, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.de1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DE', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890860
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.BF', '12.BJ', '12.BN', '12.BX', '12.BY', '12.CD'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6063, -1, 6091, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.df1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DF', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890861
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.BD', '12.BP', '12.BS', '12.BW', '12.BY', '12.CA'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5639, -1, 5391, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dg1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DG', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890862
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.BC', '12.BK', '12.BO', '12.BT', '12.BW', '12.CD'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5980, -1, 6210, -1], 'generators': [54003503616859417437382, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.24.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dh1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DH', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890863
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.B', '12.K', '12.BE', '12.BL', '12.BS', '12.BT', '12.BX'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5845, -1, 5716, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.di1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890864
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.C', '12.K', '12.BB', '12.BK', '12.BR', '12.BU', '12.BY'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6252, -1, 6265, -1], 'generators': [54003503616859417437382, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108118542983424833692672], 'label': '6144.ze.24.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dj1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DJ', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229890865
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '12.BF', '12.BL', '12.BP', '12.BU', '12.BV', '12.CB'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5576, -1, 5345, -1], 'generators': [54003503616859417437382, 108169633936803137150153, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dk1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DK', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890866
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '2.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['3072.C', '3072.D', '3072.H'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.A', '4.C', '4.F', '4.I', '6.A', '8.N'], 'core': '2.B', 'coset_action_label': None, 'count': 1, 'diagramx': [739, 1489, 730, 2022], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 377740048764960017, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.2.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A', '4.C', '4.F', '4.I', '6.A'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '2500.l', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.B', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890867
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['1024.A', '1024.B', '1024.C'], 'conjugacy_class_count': 1, 'contained_in': ['2.B', '3.a1'], 'contains': ['12.A', '12.B', '12.C', '12.D', '12.G', '12.K', '12.BB', '12.BE', '12.CV'], 'core': '6.A', 'coset_action_label': None, 'count': 1, 'diagramx': [5257, 949, 5651, 309], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 377740048764960017, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.6.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': ['2.B'], 'normal_contains': ['12.A', '12.B', '12.C', '12.D', '24.A'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '2500.l', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.A', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229890868
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L', '12.BG', '12.CB'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1079, -1, 1819, -1], 'generators': [4097467157062, 53952413034673736392198, 108118165243376109012342, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 256107468811985417], 'label': '6144.ze.24.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.dl1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DL', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229890869
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.L', '12.BH', '12.CD'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1644, -1, 1990, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 51468697530548501041, 53952413034673736392198, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.dm1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DM', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229890870
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.M', '12.BG', '12.CD'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1256, -1, 2321, -1], 'generators': [4097467157062, 53952413034673736392198, 108118165243376109012342, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 256115864664974016], 'label': '6144.ze.24.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.dn1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DN', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229890871
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.M', '12.BH', '12.CB'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1034, -1, 2132, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 51468700347165007319, 53952413034673736392198, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.do1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DO', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229890872
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.G', '12.BM', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7749, -1, 8607, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dp1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DP', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890873
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '12.BM', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7694, -1, 8559, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 51468697530548501041, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dq1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DQ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890874
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '12.V', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6733, -1, 7113, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 53952412685900568952456, 54003503622465652187519, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dr1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DR', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890875
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '12.U', '12.V'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4147, -1, 4718, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 54003503622465652187519, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ds1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DS', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890876
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.BI', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7541, -1, 9300, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 53952412685900568952456, 4097467157062, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dt1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DT', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890877
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.BN', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7639, -1, 9389, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 51468697530548501041, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.du1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DU', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890878
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.E', '12.F', '12.G', '12.H', '12.N', '12.Q', '12.R', '12.S', '12.T', '12.W', '12.X', '12.Y', '12.Z', '12.BI', '12.BJ', '12.BM', '12.BN', '12.BQ', '12.BZ', '12.CM', '12.CN', '12.CR', '12.CS'], 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': [8270, -1, 7971, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890879
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.BM', '12.BN'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8615, -1, 8946, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 51468697530548501041, 51091303471599669696, 122003583856732942, 54003247884686882097359], 'label': '6144.ze.24.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dv1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DV', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890880
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '12.BQ', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7666, -1, 9415, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dw1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DW', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 229890881
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.BM', '12.BQ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8737, -1, 8975, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 53952412690199089417672, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dx1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DX', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 229890882
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.N', '12.BJ', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7485, -1, 9359, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.dy1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DY', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890883
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.DZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O', '12.U', '12.CA'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4351, -1, 3491, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dz1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DZ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890884
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O', '12.V', '12.CC'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3068, -1, 4331, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ea1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EA', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890885
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.U', '12.CC'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3924, -1, 2931, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 53952412690199089417672, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.eb1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EB', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891321
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.G'], 'contains': ['768.S'], 'core': '3072.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122000787877207687, 25903229683158464681647, 25903364133006332138897, 51091297865364924726], 'label': '6144.ze.384.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC3', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.J', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229890886
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.P', '12.V', '12.CA'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2820, -1, 2732, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ec1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EC', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890887
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.ED', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.W', '12.BI'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9116, -1, 8043, -1], 'generators': [51090957482037557056, 54003247884686882097359, 4097467157062, 53952413034673736392198, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ed1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ED', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890888
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.X', '12.BI'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7773, -1, 8248, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 377748450845332417, 53952413034673736392198, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ee1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EE', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890889
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.E', '12.J', '12.K', '12.BK', '12.BL', '12.BT', '12.BU', '12.CO'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5948, -1, 5823, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 108118542983424833692672, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.6.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.C', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890890
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.X', '12.BJ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8200, -1, 9113, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 53952413034673736392198, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.24.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ef1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EF', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890891
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.W', '12.BJ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8539, -1, 7981, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 53952413034673736392198, 122003583856732942, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.24.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.eg1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EG', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890892
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.W', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9205, -1, 8203, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 122003583856732942, 53952413029067501642303, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.24.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.eh1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EH', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890893
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.X', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8057, -1, 8698, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 122003583856732942, 53952413029067501642303, 51090957482037557056, 377740048764960017], 'label': '6144.ze.24.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ei1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EI', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890894
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.T', '12.W', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9767, -1, 8759, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 51347042732487422033, 122003583856732942, 53952413029067501642303, 51090957482037557056], 'label': '6144.ze.24.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ej1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EJ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890895
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.T', '12.X', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9699, -1, 9082, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 53952035294625185894256, 4097467157062, 122003583856732942, 53952413029067501642303, 51090957482037557056], 'label': '6144.ze.24.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ek1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EK', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890896
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.Y', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9971, -1, 9437, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 53952035294625185894256, 54003503622465652187519, 4097467157062, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.el1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EL', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890897
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.Y', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9743, -1, 8783, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 51347042732487422033, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.em1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EM', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890898
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.P', '12.S', '12.Y', '12.BI'], 'contains': ['48.B'], 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [7332, -1, 7271, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 51347041223585195521, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.en1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EN', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890899
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.Z', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9881, -1, 9501, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.24.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.eo1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EO', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890900
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.G', '12.I', '12.J', '12.BO', '12.BP', '12.BV', '12.BW', '12.CP'], 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5346, -1, 5575, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.6.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.D', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890901
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.T', '12.Z', '12.BI'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9457, -1, 8810, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 377748450845332417, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ep1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EP', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890902
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.Z', '12.BM'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9318, -1, 9051, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 122003583856732942, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.24.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.eq1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EQ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890903
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.ER', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.Q', '12.S', '12.Z', '12.BJ'], 'contains': ['48.C'], 'core': '48.C', 'coset_action_label': None, 'count': 6, 'diagramx': [7375, -1, 7691, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.24.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.er1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ER', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 229890904
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.ES', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.T', '12.Y', '12.BJ'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9828, -1, 8855, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.es1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ES', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890905
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.ET', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.X', '12.BN'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8139, -1, 9144, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 51468697530548501041, 377748450845332417, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.et1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ET', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890906
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.W', '12.BN'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8765, -1, 8007, -1], 'generators': [53952156946639855382521, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 377748450845332417, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.eu1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EU', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890907
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.W', '12.BQ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9099, -1, 8434, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 4097467157062, 53952413034673736392198, 122003583856732942, 54003247877598743421360], 'label': '6144.ze.24.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ev1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EV', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 229890908
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.X', '12.BQ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7861, -1, 8313, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 4097467157062, 53952413034673736392198, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ew1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EW', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 229890909
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.W', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7564, -1, 8384, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 53952413029067501642303, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ex1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EX', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890910
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.S', '12.X', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7517, -1, 9173, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 53952413029067501642303, 122003583856732942, 54003247877598743421360], 'label': '6144.ze.24.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ey1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EY', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890911
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.H', '12.I', '12.K', '12.BR', '12.BS', '12.BX', '12.BY', '12.CQ'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5713, -1, 5733, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 108169256206464380536342, 108118542983424833692672, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.6.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.E', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890912
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.EZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.T', '12.W', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9288, -1, 9002, -1], 'generators': [25903229683158464676480, 53952412685900568952456, 122003583856732942, 1313941668480, 1313941673647, 53952035294625185894256, 4097467157062, 53952413029067501642303], 'label': '6144.ze.24.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ez1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EZ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890913
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.T', '12.X', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8168, -1, 9257, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 51347042732487422033, 53952413029067501642303, 122003583856732942], 'label': '6144.ze.24.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fa1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FA', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890914
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.Y', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9923, -1, 9456, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503622465652187519, 4097467157062, 51347042732487422033, 122003583856732942], 'label': '6144.ze.24.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fb1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FB', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890915
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.Y', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8865, -1, 9281, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 53952035294625185894256, 54003503622465652187519, 4097467157062, 122003583856732942], 'label': '6144.ze.24.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fc1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FC', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229890916
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.R', '12.S', '12.Y', '12.BN'], 'contains': ['48.B'], 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [7453, -1, 7769, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 51347041223585195521, 54003503616859417437382, 4097467157062, 51468697530548501041, 122003583856732942], 'label': '6144.ze.24.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fd1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FD', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229890917
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.Q', '12.Z', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9522, -1, 9564, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503622465652187519, 4097467157062, 122003583856732942, 54003247877598743421360], 'label': '6144.ze.24.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fe1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FE', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890918
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.S', '12.S', '12.Z', '12.BQ'], 'contains': ['48.C'], 'core': '48.C', 'coset_action_label': None, 'count': 6, 'diagramx': [7422, -1, 7858, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ff1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FF', 'subgroup_fusion': None, 'weyl_group': '64.264'}
  • id: 229890919
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.T', '12.Y', '12.BQ'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9854, -1, 9025, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942], 'label': '6144.ze.24.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fg1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FG', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 229890920
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.R', '12.Z', '12.BZ'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8839, -1, 9326, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503622465652187519, 4097467157062, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fh1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FH', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890921
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.T', '12.Z', '12.BN'], 'contains': [], 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9488, -1, 8915, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 377748450845332417, 122003583856732942], 'label': '6144.ze.24.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fi1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FI', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890922
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A', '3.a1'], 'contains': ['12.A', '12.E', '12.I', '12.O', '12.P', '12.U', '12.V', '12.BA', '12.BD', '12.CA', '12.CC', '12.CE', '12.CF', '12.CG', '12.CH', '12.CT', '12.CX', '12.CY', '12.DM', '12.DN', '12.DO'], 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4003, -1, 3857, -1], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 51090957482037557056, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.6.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.F', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890923
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O', '12.CE', '12.CF'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4423, -1, 4627, -1], 'generators': [108169256206464380536342, 51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 108118165246159714329599, 1313941673647], 'label': '6144.ze.24.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fj1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FJ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890924
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.E', '12.CE', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4632, -1, 4767, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503618341535830447, 53952412685900568952456, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fk1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FK', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890925
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.E', '12.CF', '12.CG'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [3283, -1, 3958, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fl1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FL', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890926
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.P', '12.CE', '12.CF'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3858, -1, 3753, -1], 'generators': [6920176418617, 108118165246159714329599, 1313941668480, 25903229683158464676480, 1313941673647, 187973564326514163969982, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fm1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FM', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890927
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.I', '12.CE', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4655, -1, 4692, -1], 'generators': [6920176418617, 187973564326514163969982, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fn1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FN', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890928
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.I', '12.CF', '12.CG'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [3189, -1, 3910, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fo1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FO', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890929
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O', '12.CE', '12.CG'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4405, -1, 4287, -1], 'generators': [187922473367523358862032, 51090957482037557056, 6920176418617, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.24.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fp1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FP', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890930
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.CE'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2979, -1, 3040, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503618341535830447, 54003503622465652187519, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fq1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FQ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890931
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.P', '12.CE', '12.CG'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4026, -1, 3145, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 51091303471599669696, 187922473367523358862032, 122003583856732942], 'label': '6144.ze.24.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fr1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FR', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890932
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [6866, -1, 6800, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 122003583856732942, 51090957482037557056, 51091306255204991878, 51091299166851820921], 'label': '6144.ze.24.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '24.fs1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FS', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890933
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.C', '3.a1'], 'contains': ['12.A', '12.H', '12.J', '12.L', '12.M', '12.BC', '12.BF', '12.BG', '12.BH', '12.CB', '12.CD', '12.CU', '12.CW', '12.CZ'], 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': [2004, -1, 2489, -1], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 4097467157062, 108118165243376109012342, 54003503616859417437382, 51468697530548501041], 'label': '6144.ze.6.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.g1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.G', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890934
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6885, -1, 6819, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503618341535830447, 54003503622465652187519, 53952413034673736392198, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '24.ft1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FT', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229890935
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4768, -1, 4966, -1], 'generators': [51090957482037557056, 6920176418617, 4097467157062, 108118287248261452641239, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.fu1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890936
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4840, -1, 5167, -1], 'generators': [51090957482037557056, 122010491578389112, 4097467157062, 108118287248261452641239, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.fu2', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229890937
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O', '12.CF', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4369, -1, 4225, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941668480, 1313941673647, 108118165250283830616367, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fv1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FW', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890938
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.P', '12.CF', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4000, -1, 3513, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941668480, 1313941673647, 187973564326514163969982, 108118165250283830616367, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fw1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FX', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890939
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2009, -1, 2649, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 53952413034673736392198, 122003583856732942, 108118165243376109012342, 51091306255204991878], 'label': '6144.ze.24.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '24.fx1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FY', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 229890940
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.FZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.CF'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 6, 'diagramx': [2626, -1, 2882, -1], 'generators': [6920176418617, 108118165246159714329599, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.FZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fy1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FZ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890941
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O', '12.CG', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4387, -1, 3609, -1], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 51090954698471793966, 108118165243376109012342], 'label': '6144.ze.24.GA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.fz1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GA', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890942
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.P', '12.CG', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3831, -1, 2983, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 51091303471599669696, 53952412687382647065606, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.GB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ga1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GB', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890943
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.T', '12.A', '12.CG'], 'contains': ['48.D'], 'core': '48.D', 'coset_action_label': None, 'count': 2, 'diagramx': [2245, -1, 2226, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.GC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '24.gb1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GC', 'subgroup_fusion': None, 'weyl_group': '384.20163'}
  • id: 229890944
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.BA', '12.BB', '12.BC', '12.BI', '12.BK', '12.BO', '12.BR', '12.CI', '12.CJ', '12.DA', '12.DP'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [6073, -1, 6233, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108118542983424833692672, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.6.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.H', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890945
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4894, -1, 4860, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 51091303471599669696, 108118165243376109012342, 51090957482037557056], 'label': '6144.ze.24.GD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.gc1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GD', 'subgroup_fusion': None, 'weyl_group': '64.261'}
  • id: 229890946
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2917, -1, 2865, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503618341535830447, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.GE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gd1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GE', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229890947
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.O'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4876, -1, 4842, -1], 'generators': [51090957482037557056, 122010491578389112, 4097467157062, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.GF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.ge1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229890948
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.U', '12.CF', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4173, -1, 3679, -1], 'generators': [1313941668480, 108118165246159714329599, 25903229683158464676480, 1313941673647, 108169256206464380536342, 54003503622465652187519, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.GG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gf1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890949
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BA', '12.CF', '12.CG'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [3163, -1, 3936, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 108118165250283830616367, 51091303471599669696, 122003583856732942, 51090954698471793966], 'label': '6144.ze.24.GH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gg1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GH', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890950
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.V', '12.CF', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3304, -1, 4101, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941668480, 1313941673647, 187973564326514163969982, 54003503622465652187519, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gh1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890951
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BD', '12.CF', '12.CG'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [3448, -1, 3883, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 108169256202366873835447, 108118165250283830616367, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.GJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gi1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GJ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890952
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.U', '12.CG', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4200, -1, 3241, -1], 'generators': [187922473367523358862032, 51090957482037557056, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.GK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gj1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GK', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890953
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.V', '12.CG', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3019, -1, 3587, -1], 'generators': [187922473367523358862032, 53952412685900568952456, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.GL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gk1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GL', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890954
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BG'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1230, -1, 2613, -1], 'generators': [378113869110326273, 1313941668480, 25903229683158464676480, 108118287248261452641239, 6920176418617, 187973563958306240457616, 1313941673647, 4097467157062], 'label': '6144.ze.24.GM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '24.gl1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GM', 'subgroup_fusion': None, 'weyl_group': '128.1135'}
  • id: 229890955
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.BA', '12.BE', '12.BF', '12.BJ', '12.BL', '12.BV', '12.BX', '12.DB'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5321, -1, 5599, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.6.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.i1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.I', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890956
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BG'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1117, -1, 2537, -1], 'generators': [378113869110326273, 1313941668480, 25903229683158464676480, 108118287248261452641239, 187973563958306240457616, 1313941673647, 122010491578389112, 4097467157062], 'label': '6144.ze.24.GN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '24.gl2', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GN', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 229890957
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BC'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [6147, -1, 6159, -1], 'generators': [54003503616859417437382, 108118165250283830616367, 51091306255204991878, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.24.GO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BC', 'old_label': '24.gm1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GO', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 229890958
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BB'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6556, -1, 6326, -1], 'generators': [108118165250283830616367, 53952413034673736392198, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.GP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BB', 'old_label': '24.gn1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GP', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229890959
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BA', '12.CH', '12.CI'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5692, -1, 5493, -1], 'generators': [108118165250283830616367, 53952412685900568952456, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.GQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.go1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GQ', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 229890960
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BB', '12.CI'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6652, -1, 6361, -1], 'generators': [108118165250283830616367, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.GR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.gp1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GR', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890961
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BC', '12.CI'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6450, -1, 6287, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169633946512931760000, 54003503618341535830447, 108118165250283830616367, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.GS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.gq1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GS', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 229890962
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BD', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5157, -1, 4668, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 54003503618341535830447, 108118165250283830616367, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.GT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gr1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GT', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 229890963
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BG'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1098, -1, 2518, -1], 'generators': [53952291036669465204456, 378113869110326273, 6920176418617, 4097467157062, 108118165243376109012342, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.GU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '24.gs1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GU', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 229890964
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.U', '12.CE', '12.CF'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4098, -1, 3981, -1], 'generators': [1313941668480, 108118165246159714329599, 25903229683158464676480, 1313941673647, 108169256206464380536342, 51091303471599669696, 187922473373129593564937, 122003583856732942], 'label': '6144.ze.24.GV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.gt1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GV', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890965
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BI', '12.CI', '12.CJ'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6999, -1, 6705, -1], 'generators': [51090957482037557056, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.GW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.gu1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GW', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891348
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '512.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.H', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['256.D', '256.F'], 'contains': ['1024.A', '1536.Z'], 'core': '6144.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [25903107682370587473960, 242140465572991644960126, 51090954698471793966], 'label': '6144.ze.512.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.J', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.B', 'old_label': '512.d1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.C', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229890966
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.BB', '12.BD', '12.BF', '12.BN', '12.BP', '12.BU', '12.BY', '12.DC'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [5374, -1, 5675, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 108118542983424833692672, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.6.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.j1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.J', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890967
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BA', '12.CE', '12.CJ'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5782, -1, 5520, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503618341535830447, 53952412685900568952456, 51091303471599669696, 187922473373129593564937, 122003583856732942], 'label': '6144.ze.24.GX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.gv1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GX', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890968
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BK', '12.CI', '12.CJ'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6923, -1, 6485, -1], 'generators': [51090957482037557056, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.GY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.gw1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GY', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890969
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.GZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CA', '12.CF', '12.CK'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 6, 'diagramx': [2581, -1, 1881, -1], 'generators': [1313941668480, 108118165246159714329599, 25903229683158464676480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.GZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.gx1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.GZ', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890970
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BI', '12.CK', '12.CL'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [932, -1, 1232, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 377748450845332417, 51091303471599669696, 122003583856732942, 51090954698471793966], 'label': '6144.ze.24.HA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.gy1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HA', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890971
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BL', '12.CK', '12.CL'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [972, -1, 1194, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108118542993128400914047, 54003503616859417437382, 51091303471599669696, 122003583856732942, 51090954698471793966], 'label': '6144.ze.24.HB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.gz1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HB', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 229890972
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.V', '12.CE', '12.CF'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3238, -1, 4309, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941668480, 1313941673647, 187973564326514163969982, 51091303471599669696, 187922473373129593564937, 122003583856732942], 'label': '6144.ze.24.HC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ha1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HC', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890973
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BB', '12.CJ'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6961, -1, 6503, -1], 'generators': [187922473373129593564937, 51091303471599669696, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.HD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.hb1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HD', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890974
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BO', '12.CI', '12.CJ'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6943, -1, 6447, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169633946512931760000, 54003503618341535830447, 51091303471599669696, 122003583856732942, 54003247884686882097359], 'label': '6144.ze.24.HE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.hc1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HE', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890975
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BC', '12.CJ'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6496, -1, 6402, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169633946512931760000, 54003503618341535830447, 51091303471599669696, 187922473373129593564937, 122003583856732942], 'label': '6144.ze.24.HF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.hd1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HF', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 229890976
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.CB'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [677, -1, 1596, -1], 'generators': [25903229683158464676480, 51091306255204991878, 122003583856732942, 1313941668480, 1313941673647, 51468700347165007319, 53952413034673736392198, 108118165243376109012342], 'label': '6144.ze.24.HG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CB', 'old_label': '24.he1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890977
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '2.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['3072.B', '3072.C', '3072.D'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.A', '4.D', '4.G', '4.J', '6.G', '8.M', '8.O'], 'core': '2.C', 'coset_action_label': None, 'count': 1, 'diagramx': [521, 2771, 834, 6992], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382, 51468697530548501041], 'label': '6144.ze.2.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A', '4.D', '4.G', '4.J'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '2500.l', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.C', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229890978
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.BC', '12.BD', '12.BE', '12.BQ', '12.BS', '12.BT', '12.BW', '12.DD'], 'core': '48.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5764, -1, 5850, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.6.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.k1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.K', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229890979
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BR', '12.CI', '12.CJ'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6904, -1, 6521, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503618341535830447, 108118542983424833692672, 51091303471599669696, 122003583856732942, 187973564319600214982398], 'label': '6144.ze.24.HH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.hf1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HH', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890980
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BD', '12.CE'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5181, -1, 5010, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108169256206464380536342, 54003503618341535830447, 51091303471599669696, 187922473373129593564937, 122003583856732942], 'label': '6144.ze.24.HI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hg1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890981
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BG'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1156, -1, 2575, -1], 'generators': [53952291036669465204456, 378113869110326273, 122010491578389112, 4097467157062, 108118165243376109012342, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.24.HJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '24.hh1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HJ', 'subgroup_fusion': None, 'weyl_group': '128.1135'}
  • id: 229890982
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.B', '12.CK'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 6, 'diagramx': [1192, -1, 1295, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941668480, 1313941673647, 54003503616859417437382, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.HK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.hi1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HK', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890983
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.CB', '12.CK'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 6, 'diagramx': [752, -1, 1273, -1], 'generators': [1313941668480, 108118165246159714329599, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 51468700347165007319, 122003583856732942], 'label': '6144.ze.24.HL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.hj1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HL', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890984
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.CC', '12.CF'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 6, 'diagramx': [2774, -1, 2957, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941668480, 1313941673647, 51090961780558017359, 54003503616859417437382, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.HM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hk1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HM', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890985
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BP', '12.CK', '12.CL'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [991, -1, 1156, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 108169256202366873835447, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.HN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.hl1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HN', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890986
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BS', '12.CK', '12.CL'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [952, -1, 1213, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 108118542993128400914047, 54003503616859417437382, 108169256202366873835447, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.HO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.hm1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HO', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 229890987
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CA', '12.CE', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4306, -1, 3451, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503618341535830447, 53952412685900568952456, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.HP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hn1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HP', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890988
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.U', '12.CE', '12.CG'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4253, -1, 3342, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.HQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ho1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HQ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890989
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.D', '3.a1'], 'contains': ['12.B', '12.BI', '12.BL', '12.BP', '12.BS', '12.CA', '12.CB', '12.CK', '12.CL', '12.DE', '12.DI', '12.DQ', '12.DR'], 'core': '12.B', 'coset_action_label': None, 'count': 3, 'diagramx': [2211, -1, 2014, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056], 'label': '6144.ze.6.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.l1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.L', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890990
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CC', '12.CE', '12.CH'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4280, -1, 3561, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503618341535830447, 53952412690199089417672, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.HR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hp1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HR', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229890991
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.V', '12.CE', '12.CG'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3046, -1, 4077, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 53952412685900568952456, 54003503622465652187519, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.HS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hq1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HS', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890992
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.B', '12.CA', '12.CG', '12.CL'], 'contains': ['48.D'], 'core': '48.D', 'coset_action_label': None, 'count': 6, 'diagramx': [2397, -1, 1093, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090954698471793966], 'label': '6144.ze.24.HT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.hr1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HT', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229890993
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.U', '12.B', '12.CL'], 'contains': ['48.D'], 'core': '48.D', 'coset_action_label': None, 'count': 2, 'diagramx': [654, -1, 1012, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.HU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '24.hs1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HU', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 229890994
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.V', '12.CB', '12.CL'], 'contains': ['48.D'], 'core': '48.D', 'coset_action_label': None, 'count': 6, 'diagramx': [595, -1, 990, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 51468700347165007319, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.HV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.ht1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HV', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229890995
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.W', '12.CC', '12.CG'], 'contains': ['48.D'], 'core': '48.D', 'coset_action_label': None, 'count': 6, 'diagramx': [2443, -1, 1945, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 51090961780558017359, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.HW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.hu1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HW', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229890996
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BI'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [7199, -1, 6856, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 51347041223585195521, 54003503616859417437382, 122003583856732942, 51090957482037557056, 51091306255204991878], 'label': '6144.ze.24.HX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '24.hv1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HX', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890997
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BI'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7246, -1, 6875, -1], 'generators': [51090957482037557056, 54003247884686882097359, 53952413034673736392198, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.HY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '24.hw1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HY', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229890998
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.HZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BT'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 12, 'diagramx': [6214, -1, 6724, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 51091306255204991878, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.24.HZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BT', 'old_label': '24.hx1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.HZ', 'subgroup_fusion': None, 'weyl_group': '64.32'}
  • id: 229890999
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BU'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6350, -1, 6118, -1], 'generators': [51090961780558017359, 53952413034673736392198, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.IA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BU', 'old_label': '24.hy1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IA', 'subgroup_fusion': None, 'weyl_group': '128.850'}
  • id: 229891000
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.E', '3.a1'], 'contains': ['12.C', '12.BJ', '12.BK', '12.BW', '12.BY', '12.CA', '12.CD', '12.DF', '12.DJ'], 'core': '12.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5281, -1, 5623, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342, 51090957482037557056, 377740048764960017], 'label': '6144.ze.6.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.m1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.M', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891001
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.F'], 'contains': [], 'core': '6144.a1', 'coset_action_label': '24T9107', 'count': 96, 'diagramx': [8420, -1, 9935, -1], 'generators': [6920176418617, 1313941668480, 1313941673647, 25903364133006332138897, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.IB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.F', 'old_label': '24.hz1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IB', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891002
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.W'], 'contains': [], 'core': '6144.a1', 'coset_action_label': '24T9229', 'count': 96, 'diagramx': [9076, -1, 8226, -1], 'generators': [6920176418617, 1313941668480, 1313941673647, 79804051672210232750640, 4097467157062, 25903107685154192786062, 25852138754983141680143, 53952413034673736392198], 'label': '6144.ze.24.IC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '24.ia1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IC', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229891003
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.ID', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.E', '12.CM', '12.CX'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [6789, -1, 6961, -1], 'generators': [51090957482037557056, 4097467157062, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.ID', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ib1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ID', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891004
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.F', '12.CM', '12.CN'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [8272, -1, 8583, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 4097467157062, 51468697530548501041, 51091303471599669696, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.IE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ic1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IE', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891005
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.E', '12.CN', '12.CO', '12.CT', '12.CY'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5388, -1, 5772, -1], 'generators': [5606234750137, 54003503616859417437382, 51090961780558017359, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.IF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.id1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IF', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891006
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.G', '12.CM'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [7223, -1, 7585, -1], 'generators': [4097467157062, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 377740048764960017, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.IG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ie1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IG', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229891007
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.H', '12.CM'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [7127, -1, 7557, -1], 'generators': [51468697530548501041, 4097467157062, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.IH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.if1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IH', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891008
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.II', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.I', '12.CX'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [4937, -1, 5091, -1], 'generators': [4097467157062, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.II', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ig1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.II', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891009
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.L'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1736, -1, 1707, -1], 'generators': [122000787877207687, 25903229683158464676480, 53952291036669465204456, 1313941673647, 122004885343634062, 51468697530548501041, 108118165243376109012342, 51091299166851820921], 'label': '6144.ze.24.IJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.ih1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IJ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891010
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.L', '12.CU', '12.CZ'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1620, -1, 1923, -1], 'generators': [51468697530548501041, 4097467157062, 53952413034673736392198, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942, 51091297865364919801], 'label': '6144.ze.24.IK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ii1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IK', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891011
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.F', '3.a1'], 'contains': ['12.B', '12.BN', '12.BO', '12.BT', '12.BX', '12.CC', '12.CD', '12.DG', '12.DK'], 'core': '12.B', 'coset_action_label': None, 'count': 3, 'diagramx': [5065, -1, 5469, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 377748450845332417, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.6.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.n1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.N', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891012
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.M', '12.CU', '12.CZ'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1314, -1, 2107, -1], 'generators': [4097467157062, 53952413034673736392198, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942, 256115864664974016, 51091297865364919801], 'label': '6144.ze.24.IL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ij1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IL', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891013
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.N', '12.CM', '12.CN'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [8567, -1, 8357, -1], 'generators': [53952156946639855382521, 6920176418617, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.IM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ik1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IM', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891014
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.D', '12.G', '12.CN', '12.CP', '12.CV'], 'contains': ['48.E'], 'core': '48.E', 'coset_action_label': None, 'count': 12, 'diagramx': [5898, -1, 6061, -1], 'generators': [54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.IN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.il1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IN', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229891015
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.H', '12.CN', '12.CQ', '12.CW', '12.CZ'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5665, -1, 5879, -1], 'generators': [5606234750137, 54003503616859417437382, 4097467157062, 51091303471599669696, 51468700347165007319, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.IO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.im1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IO', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891016
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.I', '12.CP', '12.CQ', '12.CT', '12.CY'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5132, -1, 5321, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 108169256205150439593622, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.IP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.in1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IP', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891017
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.J', '12.CO', '12.CP', '12.CW', '12.CZ'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5023, -1, 5252, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 108169633945198990091520, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.IQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.io1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IQ', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891018
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.D', '12.K', '12.CO', '12.CQ', '12.CV'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5430, -1, 5832, -1], 'generators': [54003503616859417437382, 108118542984726321319552, 6920176418617, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.IR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ip1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IR', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229891019
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.E', '12.CR'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [8077, -1, 7215, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 51091304773086570816, 51091299166851820921], 'label': '6144.ze.24.IS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.iq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IS', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891020
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.F', '12.CR', '12.CS'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9597, -1, 8480, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 4097467157062, 122003583856732942, 51090957482037557056, 51091304773086570816, 54003247877598743421360], 'label': '6144.ze.24.IT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ir1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IT', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891021
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.E', '12.CS'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [7954, -1, 7196, -1], 'generators': [51090957482037557056, 4097467157062, 54003503615545556328262, 53952413034673736392198, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.IU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.is1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IU', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891022
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.G', '3.a1'], 'contains': ['12.C', '12.BQ', '12.BR', '12.BU', '12.BV', '12.CB', '12.CC', '12.DH', '12.DL'], 'core': '12.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5040, -1, 5550, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342, 377740048764960017], 'label': '6144.ze.6.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.o1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.O', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891023
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.L'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1690, -1, 1686, -1], 'generators': [122000787877207687, 187973563958306240457616, 51468697530548501041, 108118287248261452641239, 51091299166851820921, 25903229683158464676480, 1313941673647, 122004885343634062], 'label': '6144.ze.24.IV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.it1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IV', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891024
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.L', '12.CU', '12.CW'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1530, -1, 2245, -1], 'generators': [25903229683158464676480, 1313941673647, 187922473366221951068752, 54003503622465652187519, 4097467157062, 51468697530548501041, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.IW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.iu1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IW', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891025
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.M', '12.CU', '12.CW'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1338, -1, 2452, -1], 'generators': [4097467157062, 53952413034673736392198, 187973307875878553928360, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519, 108118165244677595913462], 'label': '6144.ze.24.IX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.iv1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IX', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891026
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.G', '12.CR', '12.CV'], 'contains': ['48.E'], 'core': '48.E', 'coset_action_label': None, 'count': 12, 'diagramx': [7070, -1, 7173, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942, 51091304773086570816], 'label': '6144.ze.24.IY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.iw1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IY', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229891027
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.IZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.H', '12.CR'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [7978, -1, 7370, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 122003583856732942, 51091304773086570816, 51091299166851820921], 'label': '6144.ze.24.IZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ix1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.IZ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891028
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.K', '12.CV'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5950, -1, 5980, -1], 'generators': [108169256548149195535926, 54003503616859417437382, 4097467157062, 51091299166851820921, 25903229683158464676480, 1313941673647, 51347042732487422033, 122003583856732942], 'label': '6144.ze.24.JA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.iy1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JA', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 229891029
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.N', '12.CR', '12.CS'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9620, -1, 8457, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 122003583856732942, 51091304773086570816, 54003247877598743421360], 'label': '6144.ze.24.JB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.iz1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JB', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891030
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.G', '12.CS'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [7308, -1, 7475, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503615545556328262, 54003503622465652187519, 4097467157062, 53952413034673736392198, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.JC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ja1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JC', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229891031
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.H', '12.CS', '12.CU'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [6691, -1, 6937, -1], 'generators': [53952156946639855382521, 25903229683158464676480, 6920176418617, 1313941673647, 54003503615545556328262, 4097467157062, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.JD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.jb1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JD', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891032
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.J', '12.CU'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [2870, -1, 3807, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503615545556328262, 54003503622465652187519, 4097467157062, 53952413034673736392198, 122003583856732942, 187973307875878553928360], 'label': '6144.ze.24.JE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.jc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JE', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891033
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['3.a1'], 'contains': ['12.CN', '12.CO', '12.CP', '12.CQ', '12.CT', '12.CV', '12.CW', '12.DA', '12.DB', '12.DC', '12.DD', '12.DE', '12.DF', '12.DG', '12.DH'], 'core': '48.E', 'coset_action_label': None, 'count': 24, 'diagramx': [5232, -1, 5513, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 108118542983424833692672, 54003503616859417437382, 4097467157062, 108118165244677595913462, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.6.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.p1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.P', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891034
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [4750, -1, 4931, -1], 'generators': [122000787877207687, 51090957482037557056, 6920176418617, 108118287248261452641239, 51091303471599669696, 25903229683158464676480, 1313941673647, 122004885343634062], 'label': '6144.ze.24.JF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.jd1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891035
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.O', '12.CT', '12.CX'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [4547, -1, 4807, -1], 'generators': [108118165250283830616367, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.JG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.je1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JG', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891036
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.P', '12.CT', '12.CX'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [3949, -1, 4144, -1], 'generators': [108118165250283830616367, 4097467157062, 187973564326514163969982, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.JH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.jf1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JH', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891037
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [4696, -1, 4878, -1], 'generators': [122000787877207687, 51090957482037557056, 6920176418617, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122004885343634062], 'label': '6144.ze.24.JI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.jg1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JI', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891038
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.O', '12.CX', '12.CY'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [3471, -1, 4269, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 4097467157062, 51090956180549930176, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.JJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.jh1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JJ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891039
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.P', '12.CX', '12.CY'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 24, 'diagramx': [3493, -1, 3289, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 53952412684586628009736, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.JK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ji1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JK', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891040
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.A', '12.CU'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1783, -1, 2190, -1], 'generators': [51091304773086570816, 4097467157062, 53952413034673736392198, 51091299166851820921, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.JL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.jj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JL', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 229891041
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.A', '12.CT', '12.CV', '12.CW'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 6, 'diagramx': [2997, -1, 4503, -1], 'generators': [54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.JM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.jk1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JM', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229891042
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.A', '12.CX'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 12, 'diagramx': [2670, -1, 3023, -1], 'generators': [4097467157062, 54003503615545556328262, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.JN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.jl1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JN', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891043
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.Q', '12.CM', '12.CR'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9905, -1, 8647, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 53952413035975144185478, 122003583856732942, 54003247877598743421360, 51091299166851820921], 'label': '6144.ze.24.JO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.jm1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JO', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891063
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.Z', '12.CM', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9555, -1, 8671, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503615545556328262, 4097467157062, 122003583856732942, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.24.KG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ke1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KG', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229891044
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.H', '3.a1'], 'contains': ['12.D', '12.CN', '12.CO', '12.CP', '12.CQ', '12.CY', '12.CZ', '12.DA', '12.DB', '12.DC', '12.DD', '12.DI', '12.DJ', '12.DK', '12.DL'], 'core': '12.D', 'coset_action_label': None, 'count': 24, 'diagramx': [5013, -1, 5441, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942, 377741362626794897], 'label': '6144.ze.6.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.q1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.Q', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891045
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.R', '12.CM', '12.CR'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9417, -1, 8497, -1], 'generators': [51090957482037557056, 54003247877598743421360, 4097467157062, 51091299166851820921, 25903229683158464676480, 1313941673647, 122003583856732942, 53952413035975144185478], 'label': '6144.ze.24.JP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.jn1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JP', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891046
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.Q', '12.CN', '12.CS'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9657, -1, 7942, -1], 'generators': [51090957482037557056, 54003247884686882097359, 4097467157062, 53952413034673736392198, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.JQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.jo1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JQ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891047
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.R', '12.CN', '12.CS'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [8715, -1, 7732, -1], 'generators': [54003247884686882097359, 53952412685900568952456, 4097467157062, 53952413034673736392198, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.JR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.jp1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JR', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891048
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.S', '12.CM', '12.CS'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9222, -1, 7912, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503615545556328262, 4097467157062, 122003583856732942, 54003247877598743421360, 51091299166851820921], 'label': '6144.ze.24.JS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.jq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JS', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229891049
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.X', '12.S', '12.CN', '12.CR'], 'contains': ['48.E'], 'core': '48.E', 'coset_action_label': None, 'count': 48, 'diagramx': [7397, -1, 7077, -1], 'generators': [51090957482037557056, 54003503616859417437382, 4097467157062, 51347041223585195521, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.JT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.jr1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JT', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229891050
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.T', '12.CM', '12.CS'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9641, -1, 8110, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412685900568952456, 53952035294625185894256, 54003503615545556328262, 4097467157062, 122003583856732942, 53952413029067501642303], 'label': '6144.ze.24.JU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.js1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JU', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891051
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.T', '12.CN', '12.CR'], 'contains': [], 'core': '96.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9785, -1, 7897, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 51347044033975048913, 4097467157062, 377748450845332417, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.JV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.jt1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JV', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891052
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.U', '12.CT', '12.CX'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 24, 'diagramx': [4122, -1, 4206, -1], 'generators': [4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942, 54003503622465652187519, 108118165244677595913462], 'label': '6144.ze.24.JW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ju1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JW', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891053
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.V', '12.CT', '12.CX'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 24, 'diagramx': [3597, -1, 4787, -1], 'generators': [53952412685900568952456, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519, 108118165244677595913462], 'label': '6144.ze.24.JX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.jv1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JX', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891054
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.U', '12.CX', '12.CY'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 24, 'diagramx': [3352, -1, 3427, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503622465652187519, 4097467157062, 51090956180549930176, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.JY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.jw1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JY', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891055
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.A', '4.B', '4.C', '4.D', '4.E', '4.F', '4.G'], 'contains': ['16.A', '16.B', '16.C', '24.B', '32.E', '32.H', '32.K'], 'core': '8.A', 'coset_action_label': None, 'count': 1, 'diagramx': [803, 5905, 748, 4683], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.8.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': ['4.A', '4.B', '4.C', '4.D', '4.E', '4.F', '4.G'], 'normal_contains': ['16.A', '16.B', '16.C', '24.B'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.A', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891056
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.JZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.V', '12.CX', '12.CY'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 24, 'diagramx': [3214, -1, 4184, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412684586628009736, 54003503622465652187519, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.JZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.jx1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.JZ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891057
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.W', '12.CM', '12.CR'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9400, -1, 7959, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 4097467157062, 53952413035975144185478, 122003583856732942, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.24.KA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.jy1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KA', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891058
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.X', '12.CM', '12.CR'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9380, -1, 8515, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 53952412685900568952456, 53952413035975144185478, 4097467157062, 122003583856732942, 54003247877598743421360], 'label': '6144.ze.24.KB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.jz1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KB', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891059
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.W', '12.CN', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9186, -1, 7715, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 377748450845332417, 53952413034673736392198, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.KC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ka1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KC', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891060
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.X', '12.CN', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [7832, -1, 7797, -1], 'generators': [25903229683158464676480, 1313941673647, 4097467157062, 51468697530548501041, 377748450845332417, 53952413034673736392198, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.KD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.kb1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KD', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891061
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.Y', '12.CM', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9674, -1, 8630, -1], 'generators': [51090957482037557056, 4097467157062, 54003503615545556328262, 25903229683158464676480, 1313941673647, 53952035294625185894256, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.KE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.kc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KE', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891062
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.Y', '12.CN', '12.CR'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 48, 'diagramx': [9801, -1, 8060, -1], 'generators': [25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 51347044033975048913, 4097467157062, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.KF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.kd1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KF', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891064
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.Z', '12.CN', '12.CR'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 48, 'diagramx': [9352, -1, 8086, -1], 'generators': [51090957482037557056, 54003503616859417437382, 4097467157062, 377748450845332417, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.KH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.kf1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KH', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229891065
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BA', '12.CX'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [4612, -1, 5148, -1], 'generators': [108118165250283830616367, 53952412685900568952456, 4097467157062, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.KI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.kg1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891066
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['768.R', '768.S', '768.T', '768.U', '768.V', '768.W', '768.X', '768.Z', '768.Y', '768.BB', '768.BA', '768.BC'], 'conjugacy_class_count': 2, 'contained_in': ['4.B', '4.P', '4.Q'], 'contains': ['16.A', '16.D', '24.HT', '32.P', '32.R'], 'core': '8.B', 'coset_action_label': None, 'count': 2, 'diagramx': [2220, 8527, 894, 8250], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 51090957482037557056, 242140587575261560029503, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.8.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': ['4.B'], 'normal_contains': ['16.A', '16.D'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '2500.l', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.B', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891067
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BA', '12.CT', '12.CY', '12.DA', '12.DB'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5265, -1, 5367, -1], 'generators': [54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 51090956180549930176], 'label': '6144.ze.24.KJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.kh1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KJ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891068
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BD', '12.CX'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5108, -1, 4986, -1], 'generators': [108118165250283830616367, 4097467157062, 54003503615545556328262, 187973564326514163969982, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.KK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ki1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KK', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891069
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BG', '12.CU', '12.CZ'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1378, -1, 2154, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 4097467157062, 53952413034673736392198, 122003583856732942, 256114563257180736, 108118165243376109012342], 'label': '6144.ze.24.KL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.kj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KL', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891070
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BH', '12.CU', '12.CZ'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1464, -1, 2083, -1], 'generators': [5606234750137, 4097467157062, 53952413034673736392198, 108118165243376109012342, 51468700347165007319, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.KM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.kk1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KM', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891071
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.D', '12.BB', '12.CV', '12.DA', '12.DC'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5715, -1, 5935, -1], 'generators': [54003503616859417437382, 108118542984726321319552, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.KN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.kl1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KN', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229891072
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BC', '12.CW', '12.CZ', '12.DA', '12.DD'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5554, -1, 5452, -1], 'generators': [54003503616859417437382, 4097467157062, 51091303471599669696, 51468700347165007319, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165248982343715247], 'label': '6144.ze.24.KO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.km1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KO', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229891073
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BD', '12.CT', '12.CY', '12.DC', '12.DD'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5086, -1, 5278, -1], 'generators': [54003503616859417437382, 51090961780558017359, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165248982343715247], 'label': '6144.ze.24.KP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.kn1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KP', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229891074
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.D', '12.BE', '12.CV', '12.DB', '12.DD'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [5406, -1, 5809, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.KQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ko1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KQ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891075
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BF', '12.CW', '12.CZ', '12.DB', '12.DC'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [4914, -1, 5226, -1], 'generators': [51468696229140707761, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.KR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.kp1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KR', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891076
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BG', '12.CU', '12.CW'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1359, -1, 2473, -1], 'generators': [108118165250283830616367, 4097467157062, 53952413034673736392198, 187973307875878553928360, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.KS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.kq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KS', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891077
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['768.O', '768.N', '768.P', '768.Q'], 'conjugacy_class_count': 2, 'contained_in': ['4.A', '4.H', '4.I', '4.J'], 'contains': ['16.B', '16.BI', '24.C', '32.W', '32.Y', '32.Z'], 'core': '8.C', 'coset_action_label': None, 'count': 2, 'diagramx': [776, 2449, 872, 4076], 'generators': [5606234750137, 25903229683158464676480, 242140587575261560029503, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.8.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': ['4.A', '4.H', '4.I', '4.J'], 'normal_contains': ['16.B', '24.C'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '6144.ze', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.C', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891078
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BH', '12.CU', '12.CW'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 24, 'diagramx': [1507, -1, 2407, -1], 'generators': [108118165250283830616367, 51468697530548501041, 4097467157062, 53952413034673736392198, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.KT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.kr1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KT', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891079
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BB', '12.CV'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6037, -1, 6247, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 108118165244677595913462, 51347042732487422033, 122003583856732942], 'label': '6144.ze.24.KU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.ks1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KU', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 229891080
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BE', '12.CV'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [5921, -1, 5952, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 108118165250283830616367, 4097467157062, 51347042732487422033, 122003583856732942, 51091304773086570816], 'label': '6144.ze.24.KV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.kt1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229891081
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BC', '12.CU'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [3136, -1, 4564, -1], 'generators': [108118165250283830616367, 4097467157062, 54003503615545556328262, 53952413034673736392198, 25903229683158464676480, 1313941673647, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.24.KW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.ku1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KW', 'subgroup_fusion': None, 'weyl_group': '128.1758'}
  • id: 229891082
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BF', '12.CU'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [2727, -1, 2757, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503615545556328262, 108118165250283830616367, 4097467157062, 51468697530548501041, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.KX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.kv1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KX', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891083
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CA', '12.CT', '12.DE', '12.DF'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 6, 'diagramx': [4590, -1, 4442, -1], 'generators': [54003503616859417437382, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.KY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.kw1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KY', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891084
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.KZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BI', '12.CM'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [8002, -1, 7252, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503615545556328262, 4097467157062, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.KZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.kx1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.KZ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891085
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BJ', '12.CM'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [7594, -1, 7645, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503615545556328262, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.LA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ky1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LA', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229891086
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.BM', '12.CM', '12.CN'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9238, -1, 7882, -1], 'generators': [54003247884686882097359, 51468697530548501041, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.LB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.kz1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LB', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891087
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BI', '12.CN', '12.DA', '12.DE', '12.DI'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5827, -1, 5856, -1], 'generators': [54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 51090956180549930176], 'label': '6144.ze.24.LC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.la1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LC', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891088
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '2.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['3072.E', '3072.F', '3072.G', '3072.D'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.B', '4.C', '4.D', '4.K', '4.Q', '4.S', '6.L', '8.P'], 'core': '2.D', 'coset_action_label': None, 'count': 1, 'diagramx': [588, 5126, 648, 6329], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 377748450845332417, 1313941673647, 51090957482037557056, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.2.D', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.B', '4.C', '4.D', '4.K'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '2500.l', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.D', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891089
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.B', '4.H', '4.K', '4.L'], 'contains': ['16.B', '16.D', '24.ME', '32.BA', '32.BC'], 'core': '8.D', 'coset_action_label': None, 'count': 2, 'diagramx': [1781, 7175, 774, 7036], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51090956180549930176, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.8.D', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.D', 'normal_contained_in': ['4.B', '4.H', '4.K', '4.L'], 'normal_contains': ['16.B', '16.D'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.D', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891090
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BJ', '12.CN', '12.DB', '12.DF', '12.DJ'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [5462, -1, 5909, -1], 'generators': [51090957482037557056, 54003503616859417437382, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.LD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lb1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LD', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891091
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BK', '12.CO', '12.DA', '12.DF', '12.DJ'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5488, -1, 5753, -1], 'generators': [51090957482037557056, 54003503616859417437382, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118542983424833692672], 'label': '6144.ze.24.LE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.L', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LE', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891092
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BL', '12.CO', '12.DB', '12.DE', '12.DI'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [4998, -1, 5205, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 51090956180549930176], 'label': '6144.ze.24.LF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ld1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LF', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891093
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CB', '12.CU'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1059, -1, 1799, -1], 'generators': [51091304773086570816, 4097467157062, 53952413034673736392198, 108118165243376109012342, 51468700347165007319, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.LG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.le1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LG', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891094
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CD', '12.CU'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1713, -1, 2060, -1], 'generators': [51091304773086570816, 4097467157062, 53952413034673736392198, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942, 256115864664974016], 'label': '6144.ze.24.LH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '24.lf1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LH', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891095
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.B', '12.CV', '12.DE', '12.DG'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 6, 'diagramx': [4979, -1, 4462, -1], 'generators': [54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.LI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lg1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LI', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229891096
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CB', '12.CW', '12.DE', '12.DH'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 6, 'diagramx': [2465, -1, 4420, -1], 'generators': [54003503616859417437382, 108169633936803137150153, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.LJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lh1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LJ', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891097
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CC', '12.CT', '12.DG', '12.DH'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 6, 'diagramx': [4567, -1, 4522, -1], 'generators': [54003503616859417437382, 108169256199550431553913, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.LK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.li1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LK', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891098
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.C', '12.CV', '12.DF', '12.DH'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 6, 'diagramx': [5285, -1, 5645, -1], 'generators': [54003503616859417437382, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462, 108118542983424833692672], 'label': '6144.ze.24.LL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LL', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229891099
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CD', '12.CW', '12.DF', '12.DG'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 6, 'diagramx': [3089, -1, 4482, -1], 'generators': [54003503616859417437382, 51468697530548501041, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.LM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lk1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LM', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891100
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['768.E', '768.D', '768.F', '768.G', '768.M', '768.J', '768.L', '768.K', '768.I', '768.H'], 'conjugacy_class_count': 2, 'contained_in': ['4.C', '4.I', '4.K', '4.M'], 'contains': ['16.B', '16.BJ', '24.D', '32.BF'], 'core': '8.E', 'coset_action_label': None, 'count': 2, 'diagramx': [688, 4552, 683, 2936], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.8.E', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.E', 'normal_contained_in': ['4.C', '4.I', '4.K', '4.M'], 'normal_contains': ['16.B', '24.D'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '6144.ze', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.E', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891101
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BN', '12.CM'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [8307, -1, 7747, -1], 'generators': [54003247884686882097359, 51468697530548501041, 4097467157062, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.LN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ll1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LN', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891102
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BQ', '12.CM'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [8038, -1, 7834, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503615545556328262, 4097467157062, 53952412690199089417672, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.24.LO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.lm1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LO', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 229891103
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.BZ', '12.CM', '12.CN'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [7618, -1, 8265, -1], 'generators': [53952156946639855382521, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519, 377741362626794897], 'label': '6144.ze.24.LP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ln1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LP', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891104
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BN', '12.CN', '12.DC', '12.DG', '12.DK'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5877, -1, 6025, -1], 'generators': [54003503616859417437382, 51468697530548501041, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.LQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lo1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LQ', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891105
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BO', '12.CP', '12.DA', '12.DG', '12.DK'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5615, -1, 5590, -1], 'generators': [54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.24.LR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lp1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LR', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891106
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BP', '12.CP', '12.DC', '12.DE', '12.DI'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5065, -1, 5186, -1], 'generators': [54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256205150439593622, 122003583856732942], 'label': '6144.ze.24.LS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LS', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891107
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BQ', '12.CN', '12.DD', '12.DH', '12.DL'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [5862, -1, 6040, -1], 'generators': [54003503616859417437382, 51090961780558017359, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.LT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lr1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LT', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229891108
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BR', '12.CQ', '12.DA', '12.DH', '12.DL'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5596, -1, 5791, -1], 'generators': [54003503616859417437382, 108118542984726321319552, 108169256199550431553913, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.LU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ls1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LU', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891109
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BS', '12.CQ', '12.DD', '12.DE', '12.DI'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5244, -1, 5299, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256205150439593622, 122003583856732942], 'label': '6144.ze.24.LV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lt1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LV', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229891110
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BT', '12.CO', '12.DD', '12.DG', '12.DK'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5368, -1, 5609, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 4097467157062, 108169633945198990091520, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.LW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.M', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lu1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LW', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229891111
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['768.D', '768.E', '768.F', '768.G', '768.K', '768.L', '768.M', '768.H', '768.I', '768.J'], 'conjugacy_class_count': 2, 'contained_in': ['4.D', '4.J', '4.K', '4.N'], 'contains': ['16.B', '16.BK', '24.MF', '32.BD', '32.BG'], 'core': '8.F', 'coset_action_label': None, 'count': 2, 'diagramx': [409, 3720, 619, 5896], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 51468699045757214039, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.8.F', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.F', 'normal_contained_in': ['4.D', '4.J', '4.K', '4.N'], 'normal_contains': ['16.B'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '6144.ze', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.F', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891112
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BU', '12.CO', '12.DC', '12.DH', '12.DL'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5322, -1, 5431, -1], 'generators': [54003503616859417437382, 108118542984726321319552, 108169633936803137150153, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.LX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lv1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LX', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891113
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BV', '12.CP', '12.DB', '12.DH', '12.DL'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [5303, -1, 5413, -1], 'generators': [54003503616859417437382, 108169256199550431553913, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.24.LY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lw1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LY', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891114
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.LZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BW', '12.CP', '12.DD', '12.DF', '12.DJ'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [5534, -1, 5628, -1], 'generators': [54003503616859417437382, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108169633946512931760000, 377741362626794897], 'label': '6144.ze.24.LZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lx1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.LZ', 'subgroup_fusion': None, 'weyl_group': '256.26539'}
  • id: 229891115
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BX', '12.CQ', '12.DB', '12.DG', '12.DK'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5345, -1, 5568, -1], 'generators': [51468696229140707761, 54003503616859417437382, 108118542993128400914047, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.MA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.M', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ly1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MA', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891116
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BY', '12.CQ', '12.DC', '12.DF', '12.DJ'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 12, 'diagramx': [5511, -1, 5667, -1], 'generators': [54003503616859417437382, 108118542984726321319552, 4097467157062, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942], 'label': '6144.ze.24.MB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.lz1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MB', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891117
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CA', '12.CX'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [2750, -1, 2366, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503615545556328262, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.MC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ma1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MC', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891118
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CC', '12.CX'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [2844, -1, 3082, -1], 'generators': [25903229683158464676480, 1313941673647, 51090961780558017359, 54003503615545556328262, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.MD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.mb1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MD', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891119
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.ME', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.D', '12.CA', '12.CY', '12.DI', '12.DJ'], 'contains': ['48.F'], 'core': '48.F', 'coset_action_label': None, 'count': 6, 'diagramx': [2047, -1, 2014, -1], 'generators': [54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942, 51090956180549930176], 'label': '6144.ze.24.ME', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.mc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ME', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891120
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.F', '12.CB', '12.CZ', '12.DI', '12.DL'], 'contains': ['48.F'], 'core': '48.F', 'coset_action_label': None, 'count': 6, 'diagramx': [796, -1, 1777, -1], 'generators': [51468699045757214039, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.MF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.md1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MF', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891121
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.G', '12.CC', '12.CY', '12.DK', '12.DL'], 'contains': ['48.F'], 'core': '48.F', 'coset_action_label': None, 'count': 6, 'diagramx': [2069, -1, 3217, -1], 'generators': [25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.MG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.me1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MG', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891122
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['768.O', '768.N', '768.Q', '768.P'], 'conjugacy_class_count': 2, 'contained_in': ['4.E', '4.H', '4.M', '4.N'], 'contains': ['16.B', '16.BL', '24.MG', '32.BB', '32.BH'], 'core': '8.G', 'coset_action_label': None, 'count': 2, 'diagramx': [825, 5228, 796, 5289], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 51090963094498960079, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.8.G', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.G', 'normal_contained_in': ['4.E', '4.H', '4.M', '4.N'], 'normal_contains': ['16.B'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '6144.ze', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.G', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891123
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.I', '12.CD', '12.CZ', '12.DJ', '12.DK'], 'contains': ['48.F'], 'core': '48.F', 'coset_action_label': None, 'count': 6, 'diagramx': [1904, -1, 2037, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.MH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.L', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.mf1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MH', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891124
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BI', '12.CR'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [8591, -1, 7233, -1], 'generators': [25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 51091304773086570816], 'label': '6144.ze.24.MI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.mg1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MI', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891125
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BJ', '12.CR'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [8113, -1, 7533, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942, 51090957482037557056, 51091304773086570816], 'label': '6144.ze.24.MJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.mh1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MJ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229891126
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.BM', '12.CR', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9721, -1, 8028, -1], 'generators': [25903229683158464676480, 1313941673647, 4097467157062, 122003583856732942, 53952413029067501642303, 51090957482037557056, 51091304773086570816, 54003247877598743421360], 'label': '6144.ze.24.MK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.mi1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MK', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891127
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.ML', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BI', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [8021, -1, 7060, -1], 'generators': [51090957482037557056, 54003247884686882097359, 4097467157062, 54003503615545556328262, 53952413034673736392198, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.ML', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.mj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ML', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891128
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BJ', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [7799, -1, 7506, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503615545556328262, 4097467157062, 53952413034673736392198, 122003583856732942, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.24.MM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.mk1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MM', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229891129
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BN', '12.CR'], 'contains': [], 'core': '96.C', 'coset_action_label': None, 'count': 12, 'diagramx': [8786, -1, 7669, -1], 'generators': [25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 4097467157062, 51468697530548501041, 122003583856732942, 51091304773086570816], 'label': '6144.ze.24.MN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ml1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MN', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891130
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BQ', '12.CR'], 'contains': [], 'core': '96.D', 'coset_action_label': None, 'count': 12, 'diagramx': [8338, -1, 7819, -1], 'generators': [25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942, 51091304773086570816], 'label': '6144.ze.24.MO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.mm1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MO', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 229891131
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.BZ', '12.CR', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 48, 'diagramx': [9580, -1, 8335, -1], 'generators': [25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 122003583856732942, 53952413029067501642303, 51091304773086570816, 54003247877598743421360], 'label': '6144.ze.24.MP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.mn1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MP', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891132
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BN', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [8323, -1, 7606, -1], 'generators': [53952156946639855382521, 25903229683158464676480, 1313941673647, 54003503615545556328262, 4097467157062, 377748450845332417, 53952413034673736392198, 122003583856732942], 'label': '6144.ze.24.MQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.mo1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MQ', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891133
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['768.D', '768.E', '768.F', '768.G', '768.H', '768.I', '768.J', '768.K', '768.L', '768.M', '768.N', '768.O', '768.P', '768.Q'], 'conjugacy_class_count': 2, 'contained_in': ['4.F', '4.I', '4.L', '4.N'], 'contains': ['16.B', '24.E', '32.BI'], 'core': '8.H', 'coset_action_label': None, 'count': 2, 'diagramx': [756, 3084, 704, 3506], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 377741362626794897], 'label': '6144.ze.8.H', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.H', 'normal_contained_in': ['4.F', '4.I', '4.L', '4.N'], 'normal_contains': ['16.B', '24.E'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': '6144.ze', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.H', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891134
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BQ', '12.CS'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 12, 'diagramx': [8094, -1, 7621, -1], 'generators': [25903229683158464676480, 1313941673647, 51090961780558017359, 54003503615545556328262, 4097467157062, 53952413034673736392198, 122003583856732942, 54003247877598743421360], 'label': '6144.ze.24.MR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.mp1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MR', 'subgroup_fusion': None, 'weyl_group': '128.2264'}
  • id: 229891135
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.E', '12.DM', '12.DO'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [3782, -1, 4587, -1], 'generators': [2796059363782, 51090957482037557056, 54003503616859417437382, 6920176418617, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.MS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.mq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MS', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891136
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.E', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6001, -1, 5734, -1], 'generators': [53952412685900568952456, 6920176418617, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.MT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.mr1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MT', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891137
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.I', '12.DM', '12.DO'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [3737, -1, 4375, -1], 'generators': [2796059363782, 54003503616859417437382, 6920176418617, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942], 'label': '6144.ze.24.MU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ms1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MU', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891138
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.I', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [4959, -1, 5051, -1], 'generators': [6920176418617, 54003503615545556328262, 187973564326514163969982, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.MV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.mt1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MV', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891139
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6847, -1, 6781, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503618341535830447, 54003503615545556328262, 54003503622465652187519, 53952413034673736392198, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.MW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '24.mu1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MW', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891140
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [6827, -1, 6762, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 122003583856732942, 51090957482037557056, 51091306255204991878, 51091304773086570816, 51091299166851820921], 'label': '6144.ze.24.MX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '24.mv1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MX', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891141
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [4858, -1, 4825, -1], 'generators': [51090957482037557056, 122010491578389112, 4097467157062, 108118287248261452641239, 51091303471599669696, 25903229683158464676480, 1313941673647, 122004885343634062], 'label': '6144.ze.24.MY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.mw1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MY', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891142
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.MZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.O', '12.DM', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [4441, -1, 4164, -1], 'generators': [51090957482037557056, 108118165250283830616367, 51091303471599669696, 25903229683158464676480, 1313941673647, 108118165246159714329599, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.MZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.mx1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.MZ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891143
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.P', '12.DM', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [3882, -1, 3265, -1], 'generators': [6920176418617, 187973564326514163969982, 51091303471599669696, 25903229683158464676480, 1313941673647, 108118165246159714329599, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.NA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.my1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NA', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891144
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['768.E', '768.D', '768.G', '768.F', '768.I', '768.H', '768.J', '768.L', '768.K', '768.M', '768.O', '768.N', '768.Q', '768.P'], 'conjugacy_class_count': 2, 'contained_in': ['4.G', '4.J', '4.L', '4.M'], 'contains': ['16.B', '24.MH', '32.BE', '32.BJ'], 'core': '8.I', 'coset_action_label': None, 'count': 2, 'diagramx': [577, 6540, 723, 6466], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51468696229140707761], 'label': '6144.ze.8.I', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.I', 'normal_contained_in': ['4.G', '4.J', '4.L', '4.M'], 'normal_contains': ['16.B'], 'normalizer': '1.a1', 'old_label': '8.i1', 'projective_image': '6144.ze', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.I', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891145
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.O'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [4732, -1, 4913, -1], 'generators': [51090957482037557056, 122010491578389112, 4097467157062, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122004885343634062], 'label': '6144.ze.24.NB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.mz1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NB', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891146
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.O', '12.DN', '12.DO'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [4458, -1, 3385, -1], 'generators': [2796059363782, 187922473367523358862032, 51090957482037557056, 6920176418617, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.NC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.na1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NC', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891147
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.ND', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.P', '12.DN', '12.DO'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [3804, -1, 2904, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 53952412685900568952456, 51091303471599669696, 187922473367523358862032, 2796059363782, 122003583856732942], 'label': '6144.ze.24.ND', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.nb1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ND', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891148
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.DM'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 6, 'diagramx': [2688, -1, 3005, -1], 'generators': [54003503616859417437382, 6920176418617, 51091303471599669696, 25903229683158464676480, 1313941673647, 108118165246159714329599, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.NE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.nc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NE', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891149
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [1991, -1, 2631, -1], 'generators': [51091304773086570816, 6920176418617, 53952413034673736392198, 51091306255204991878, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.NF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '24.nd1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NF', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 229891150
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.A', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [2706, -1, 2825, -1], 'generators': [6920176418617, 54003503615545556328262, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.NG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ne1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NG', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 229891151
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.Y', '12.A', '12.DO'], 'contains': ['48.G'], 'core': '48.G', 'coset_action_label': None, 'count': 2, 'diagramx': [2027, -1, 2208, -1], 'generators': [2796059363782, 54003503616859417437382, 6920176418617, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.NH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '24.nf1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NH', 'subgroup_fusion': None, 'weyl_group': '384.20163'}
  • id: 229891152
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.U', '12.DM', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [4051, -1, 3537, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941673647, 108169256206464380536342, 108118165244677595913462, 51091303471599669696, 187922473373129593564937, 122003583856732942], 'label': '6144.ze.24.NI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ng1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NI', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891153
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.V', '12.DM', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [3690, -1, 4053, -1], 'generators': [187922473373129593564937, 187973564326514163969982, 51091303471599669696, 25903229683158464676480, 1313941673647, 108118165246159714329599, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.NJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.nh1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NJ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891154
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.U', '12.DN', '12.DO'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [4074, -1, 3169, -1], 'generators': [2796059363782, 187922473367523358862032, 51090957482037557056, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.NK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ni1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NK', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891155
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['768.R', '768.S', '768.T', '768.U', '768.V', '768.W', '768.X', '768.Y', '768.Z', '768.BA', '768.BB', '768.BC'], 'conjugacy_class_count': 2, 'contained_in': ['4.B', '4.R', '4.S'], 'contains': ['16.C', '16.D', '24.OL', '32.BN', '32.BP'], 'core': '8.J', 'coset_action_label': None, 'count': 2, 'diagramx': [2198, 7851, 851, 7643], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941673647, 51090954698471793966, 242140587575261560029503, 2796059363782, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.8.J', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.J', 'normal_contained_in': ['4.B'], 'normal_contains': ['16.C', '16.D'], 'normalizer': '1.a1', 'old_label': '8.j1', 'projective_image': '6144.ze', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.J', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891156
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.V', '12.DN', '12.DO'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [3112, -1, 3366, -1], 'generators': [2796059363782, 187922473367523358862032, 53952412685900568952456, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.NL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.nj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NL', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891157
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BA', '12.DM', '12.DO'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [3668, -1, 4399, -1], 'generators': [2796059363782, 51090957482037557056, 54003503616859417437382, 108118165250283830616367, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.NM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.nk1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NM', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891158
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.BA', '12.DN', '12.DP'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5806, -1, 5544, -1], 'generators': [53952412685900568952456, 187922473373129593564937, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.NN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.nl1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NN', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891159
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BG'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [1211, -1, 2594, -1], 'generators': [53952291036669465204456, 378113869110326273, 122010491578389112, 4097467157062, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122004885343634062], 'label': '6144.ze.24.NO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '24.nm1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NO', 'subgroup_fusion': None, 'weyl_group': '128.1135'}
  • id: 229891160
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BD', '12.DM', '12.DO'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [3761, -1, 4351, -1], 'generators': [2796059363782, 54003503616859417437382, 108118165250283830616367, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942], 'label': '6144.ze.24.NP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.nn1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NP', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891161
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BB', '12.DP'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6519, -1, 6668, -1], 'generators': [187922473373129593564937, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.NQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.no1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NQ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891162
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BC', '12.DP'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6272, -1, 6426, -1], 'generators': [187922473373129593564937, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108169633946512931760000, 54003503618341535830447], 'label': '6144.ze.24.NR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.np1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NR', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 229891163
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BD', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5224, -1, 4646, -1], 'generators': [187922473373129593564937, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.NS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.nq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NS', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891164
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BB'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6575, -1, 6344, -1], 'generators': [108118165250283830616367, 54003503615545556328262, 53952413034673736392198, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.NT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BB', 'old_label': '24.nr1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NT', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 229891165
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BG'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 24, 'diagramx': [1137, -1, 2556, -1], 'generators': [378113869110326273, 25903229683158464676480, 108118287248261452641239, 187973563958306240457616, 1313941673647, 122010491578389112, 122004885343634062, 4097467157062], 'label': '6144.ze.24.NU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '24.ns1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NU', 'subgroup_fusion': None, 'weyl_group': '128.1135'}
  • id: 229891166
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A'], 'contains': ['16.E', '16.I', '16.J', '16.S', '16.T', '16.W', '16.BF', '24.W', '32.B'], 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2478, -1, 1448, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 242140587575261560029503, 6920176418617, 1313941673647, 51091303471599669696, 108118165243376109012342, 51090957482037557056], 'label': '6144.ze.8.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '8.k1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.K', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891167
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BC'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [6173, -1, 6186, -1], 'generators': [51091304773086570816, 54003503616859417437382, 108118165250283830616367, 51091306255204991878, 25903229683158464676480, 1313941673647, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.24.NV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BC', 'old_label': '24.nt1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NV', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 229891168
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CA', '12.DM', '12.DQ'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 6, 'diagramx': [2606, -1, 1966, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941673647, 54003503616859417437382, 108118165244677595913462, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.NW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.nu1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NW', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891169
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BI', '12.DQ', '12.DR'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [855, -1, 1371, -1], 'generators': [2796059363782, 51090957482037557056, 54003503616859417437382, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.NX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.nv1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NX', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891170
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BL', '12.DQ', '12.DR'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [836, -1, 1333, -1], 'generators': [2796059363782, 51090957482037557056, 54003503616859417437382, 108118542993128400914047, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.NY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.nw1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NY', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 229891171
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.NZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BI', '12.DP'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6980, -1, 6837, -1], 'generators': [51090957482037557056, 54003503615545556328262, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.NZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.nx1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.NZ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891172
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BK', '12.DP'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6408, -1, 6650, -1], 'generators': [51090957482037557056, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.OA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.ny1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OA', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891173
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.B', '12.DQ'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 6, 'diagramx': [1174, -1, 1645, -1], 'generators': [54003503616859417437382, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 108118165246159714329599, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.OB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.nz1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OB', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891174
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.CB', '12.DQ'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 6, 'diagramx': [728, -1, 1572, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941673647, 54003503616859417437382, 108118165244677595913462, 51091303471599669696, 51468700347165007319, 122003583856732942], 'label': '6144.ze.24.OC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.oa1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OC', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891175
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.CC', '12.DM'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 6, 'diagramx': [2897, -1, 3060, -1], 'generators': [54003503616859417437382, 51090961780558017359, 51091303471599669696, 25903229683158464676480, 1313941673647, 108118165246159714329599, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.OD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ob1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OD', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891176
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.CB'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [703, -1, 1623, -1], 'generators': [25903229683158464676480, 1313941673647, 51468700347165007319, 53952413034673736392198, 122003583856732942, 108118165243376109012342, 51091306255204991878, 51091304773086570816], 'label': '6144.ze.24.OE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CB', 'old_label': '24.oc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OE', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891177
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A', '4.O'], 'contains': ['16.H', '16.K', '16.P', '16.U', '16.X', '16.BG', '24.BD', '32.B'], 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': [2288, -1, 530, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 51091299166851820921], 'label': '6144.ze.8.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '8.l1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.L', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891178
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BP', '12.DQ', '12.DR'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [874, -1, 1251, -1], 'generators': [2796059363782, 54003503616859417437382, 377748450845332417, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942], 'label': '6144.ze.24.OF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.od1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OF', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891179
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BS', '12.DQ', '12.DR'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [816, -1, 1352, -1], 'generators': [2796059363782, 54003503616859417437382, 108118542993128400914047, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256202366873835447, 122003583856732942], 'label': '6144.ze.24.OG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.oe1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OG', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 229891180
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BO', '12.DP'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6389, -1, 6631, -1], 'generators': [54003247884686882097359, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108169633946512931760000, 54003503618341535830447], 'label': '6144.ze.24.OH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.of1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OH', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891181
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.BR', '12.DP'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6370, -1, 6686, -1], 'generators': [54003503615545556328262, 51091303471599669696, 187973564319600214982398, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.OI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.og1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OI', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891182
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CA', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [2937, -1, 2293, -1], 'generators': [53952412685900568952456, 54003503615545556328262, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.OJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.oh1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OJ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891183
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.CC', '12.DN'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [2959, -1, 2845, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503618341535830447, 54003503615545556328262, 53952412690199089417672, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.OK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.oi1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OK', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891184
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.J', '12.CA', '12.DO', '12.DR'], 'contains': ['48.G'], 'core': '48.G', 'coset_action_label': None, 'count': 6, 'diagramx': [2327, -1, 1117, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 2796059363782, 122003583856732942, 108118165243376109012342, 51090954698471793966], 'label': '6144.ze.24.OL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.J', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.oj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OL', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891185
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.Z', '12.B', '12.DR'], 'contains': ['48.G'], 'core': '48.G', 'coset_action_label': None, 'count': 2, 'diagramx': [617, -1, 1049, -1], 'generators': [2796059363782, 54003503616859417437382, 377748450845332417, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.OM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '24.ok1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OM', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 229891186
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.ON', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.BA', '12.CB', '12.DR'], 'contains': ['48.G'], 'core': '48.G', 'coset_action_label': None, 'count': 6, 'diagramx': [570, -1, 966, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 51468700347165007319, 2796059363782, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.24.ON', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.ol1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ON', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891187
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.BB', '12.CC', '12.DO'], 'contains': ['48.G'], 'core': '48.G', 'coset_action_label': None, 'count': 6, 'diagramx': [2421, -1, 1857, -1], 'generators': [2796059363782, 54003503616859417437382, 51090961780558017359, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.OO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.om1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OO', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891188
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.C'], 'contains': ['16.G', '16.L', '16.M', '16.BA', '24.BI', '32.D'], 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': [180, -1, 823, -1], 'generators': [122000787877207687, 187973563958306240457616, 51468697530548501041, 108118287248261452641239, 51091299166851820921, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.8.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.M', 'old_label': '8.m1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.M', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 229891189
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BI'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [7266, -1, 6894, -1], 'generators': [51090957482037557056, 54003247884686882097359, 54003503615545556328262, 53952413034673736392198, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447], 'label': '6144.ze.24.OP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '24.on1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OP', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229891190
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BI'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [7285, -1, 6913, -1], 'generators': [25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 122003583856732942, 51090957482037557056, 51091306255204991878, 51091304773086570816], 'label': '6144.ze.24.OQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '24.oo1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OQ', 'subgroup_fusion': None, 'weyl_group': '128.2194'}
  • id: 229891191
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BU'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 12, 'diagramx': [6331, -1, 6137, -1], 'generators': [51090961780558017359, 54003503615545556328262, 53952413034673736392198, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447, 108118542983424833692672], 'label': '6144.ze.24.OR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BU', 'old_label': '24.op1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OR', 'subgroup_fusion': None, 'weyl_group': '128.850'}
  • id: 229891192
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.BT'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 12, 'diagramx': [6233, -1, 6743, -1], 'generators': [51091304773086570816, 54003503616859417437382, 108118542993128400914047, 51091306255204991878, 25903229683158464676480, 1313941673647, 122003583856732942, 108169633946512931760000], 'label': '6144.ze.24.OS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BT', 'old_label': '24.oq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OS', 'subgroup_fusion': None, 'weyl_group': '64.32'}
  • id: 229891193
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CE', '12.CT', '12.DN'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [4505, -1, 4607, -1], 'generators': [53952412685900568952456, 187922473373129593564937, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447, 108118165244677595913462], 'label': '6144.ze.24.OT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.or1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OT', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891194
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CE', '12.CX', '12.DM'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [3644, -1, 4247, -1], 'generators': [6920176418617, 108118165246159714329599, 25903229683158464676480, 1313941673647, 187922473366221951068752, 187973564326514163969982, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.OU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.os1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OU', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891195
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CE', '12.CX', '12.DO'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [3377, -1, 4029, -1], 'generators': [187922473367523358862032, 53952412685900568952456, 6920176418617, 54003503619643022731567, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.OV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ot1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OV', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891196
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CE', '12.CY', '12.DN'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [4331, -1, 3405, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503618341535830447, 53952412684586628009736, 54003503622465652187519, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.OW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ou1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OW', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891197
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CG', '12.CT', '12.DM'], 'contains': [], 'core': '384.C', 'coset_action_label': None, 'count': 48, 'diagramx': [3619, -1, 4123, -1], 'generators': [54003503616859417437382, 108118165250283830616367, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256202366873835447, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.OX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ov1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OX', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891198
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CF', '12.CX', '12.DN'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [3520, -1, 3779, -1], 'generators': [51090957482037557056, 108118165250283830616367, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 108118165246159714329599, 122003583856732942], 'label': '6144.ze.24.OY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ow1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OY', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891199
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '2.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['3072.E', '3072.F', '3072.B', '3072.G', '3072.D', '3072.H'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.B', '4.F', '4.G', '4.L', '6.M', '8.Q'], 'core': '2.E', 'coset_action_label': None, 'count': 1, 'diagramx': [768, 7810, 783, 7710], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 377740048764960017, 51090957482037557056, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.2.E', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.B', '4.F', '4.G', '4.L'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '2500.l', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.E', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891200
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.B', '4.O'], 'contains': ['16.H', '16.N', '16.Q', '16.Y', '24.A', '32.C'], 'core': '24.A', 'coset_action_label': None, 'count': 4, 'diagramx': [637, -1, 314, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 377740048764960017, 51091299166851820921], 'label': '6144.ze.8.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '8.n1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.N', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891201
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.OZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CF', '12.CX', '12.DN'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [3573, -1, 3705, -1], 'generators': [6920176418617, 108118165246159714329599, 25903229683158464676480, 1313941673647, 187973564326514163969982, 54003503615545556328262, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.OZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ow2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.OZ', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891202
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CF', '12.CT', '12.DO'], 'contains': [], 'core': '384.C', 'coset_action_label': None, 'count': 48, 'diagramx': [3262, -1, 3729, -1], 'generators': [108118165247473575438719, 54003503616859417437382, 108118165250283830616367, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256206464380536342, 122003583856732942], 'label': '6144.ze.24.PA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ox1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PA', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891203
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CF', '12.CY', '12.DM'], 'contains': [], 'core': '384.C', 'coset_action_label': None, 'count': 48, 'diagramx': [3328, -1, 3857, -1], 'generators': [5606234750137, 54003503616859417437382, 51090961780558017359, 51091303471599669696, 25903229683158464676480, 1313941673647, 108118165246159714329599, 122003583856732942], 'label': '6144.ze.24.PB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.oy1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PB', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891204
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CG', '12.CX', '12.DN'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [3546, -1, 3193, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503615545556328262, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090954698471793966], 'label': '6144.ze.24.PC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.oz1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PC', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891205
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CG', '12.CX', '12.DN'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [3423, -1, 3121, -1], 'generators': [187922473367523358862032, 53952412685900568952456, 54003503615545556328262, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.PD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.oz2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PD', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891206
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.BC', '12.CG', '12.CY', '12.DO'], 'contains': [], 'core': '96.E', 'coset_action_label': None, 'count': 48, 'diagramx': [2648, -1, 2671, -1], 'generators': [5606234750137, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056], 'label': '6144.ze.24.PE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.pa1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PE', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891207
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CH', '12.CT', '12.DN'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [4527, -1, 3833, -1], 'generators': [108118165250283830616367, 53952412685900568952456, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503618341535830447, 108118165244677595913462], 'label': '6144.ze.24.PF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.pb1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PF', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891208
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CH', '12.CX', '12.DM'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [3712, -1, 4005, -1], 'generators': [187922473366221951068752, 187973564326514163969982, 51091303471599669696, 25903229683158464676480, 1313941673647, 108118165246159714329599, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.PG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.pc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891209
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CH', '12.CX', '12.DO'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [3401, -1, 3628, -1], 'generators': [187922473367523358862032, 53952412685900568952456, 54003503619643022731567, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 54003503622465652187519], 'label': '6144.ze.24.PH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.pd1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PH', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891210
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CH', '12.CY', '12.DN'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 48, 'diagramx': [4227, -1, 3315, -1], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503618341535830447, 53952412684586628009736, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.24.PI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.pe1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 229891211
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.C', '4.O'], 'contains': ['16.H', '16.O', '16.R', '16.Z', '24.BN', '32.D'], 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': [495, -1, 450, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 122003583856732942, 51091299166851820921], 'label': '6144.ze.8.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '8.o1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.O', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891212
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['12.CI', '12.DA', '12.DP'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 96, 'diagramx': [6427, -1, 6380, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503618341535830447, 108118165250283830616367, 51091303471599669696, 108118542984726321319552, 187973307875878553928360, 122003583856732942], 'label': '6144.ze.24.PJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.pf1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PJ', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891213
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CL', '12.DE', '12.DQ'], 'contains': [], 'core': '384.C', 'coset_action_label': None, 'count': 48, 'diagramx': [775, -1, 1175, -1], 'generators': [54003503616859417437382, 108118542993128400914047, 51091303471599669696, 25903229683158464676480, 1313941673647, 108169256202366873835447, 122003583856732942, 108118165244677595913462], 'label': '6144.ze.24.PK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.pg1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PK', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891214
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CK', '12.DE', '12.DR'], 'contains': [], 'core': '384.C', 'coset_action_label': None, 'count': 48, 'diagramx': [913, -1, 1137, -1], 'generators': [108118165247473575438719, 51090957482037557056, 54003503616859417437382, 108118542993128400914047, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.24.PL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.ph1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PL', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891215
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['12.CJ', '12.DA', '12.DP'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 96, 'diagramx': [6473, -1, 6540, -1], 'generators': [108118542984726321319552, 187922473373129593564937, 51091303471599669696, 25903229683158464676480, 1313941673647, 122003583856732942, 108169633946512931760000, 54003503618341535830447], 'label': '6144.ze.24.PM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.pi1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PM', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891216
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.CK', '12.DI', '12.DQ'], 'contains': [], 'core': '384.C', 'coset_action_label': None, 'count': 48, 'diagramx': [894, -1, 1314, -1], 'generators': [25903229683158464676480, 108118165246159714329599, 1313941673647, 108169256205150439593622, 54003503616859417437382, 377748450845332417, 51091303471599669696, 122003583856732942], 'label': '6144.ze.24.PN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.pj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PN', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891217
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '24.PO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.BD', '12.CL', '12.DI', '12.DR'], 'contains': [], 'core': '96.E', 'coset_action_label': None, 'count': 48, 'diagramx': [636, -1, 1031, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 51468700347165007319, 108118165243376109012342, 122003583856732942, 377749752252399937], 'label': '6144.ze.24.PO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.K', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '24.pk1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.PO', 'subgroup_fusion': None, 'weyl_group': '256.26531'}
  • id: 229891218
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['192.B', '192.C', '192.D', '192.E', '192.F', '192.G'], 'conjugacy_class_count': 1, 'contained_in': ['16.A', '16.B', '16.C', '16.D', '16.BI', '16.BJ', '16.BK', '16.BL'], 'contains': ['96.E'], 'core': '32.A', 'coset_action_label': None, 'count': 1, 'diagramx': [570, 6115, 693, 4683], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.32.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '32.A', 'normal_contained_in': ['16.A', '16.B', '16.C', '16.D'], 'normal_contains': ['96.E'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '6144.ze', 'quotient_action_image': '16.11', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '32.A', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891219
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.K', '8.L', '16.F'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [2403, -1, 531, -1], 'generators': [122000787877207687, 51090957482037557056, 51091299166851820921, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.32.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.b1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.B', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891220
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.N', '16.F'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [1883, -1, 55, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 242140587575261560029503, 1313941673647, 377740048764960017, 51091299166851820921], 'label': '6144.ze.32.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.c1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.C', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 229891221
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.M', '8.O', '16.F'], 'contains': [], 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [547, -1, 395, -1], 'generators': [122000787877207687, 51468697530548501041, 51091299166851820921, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.32.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.d1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.D', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 229891222
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.D', '4.O'], 'contains': ['16.K', '16.N', '16.O', '16.V', '16.BB', '16.BH', '24.EN', '32.F'], 'core': '48.B', 'coset_action_label': None, 'count': 4, 'diagramx': [315, -1, 223, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056], 'label': '6144.ze.8.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '8.p1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.P', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891223
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '16.E', '16.I', '16.J'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2247, -1, 1322, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 242140587575261560029503, 1313941673647, 51091303471599669696, 108118165243376109012342], 'label': '6144.ze.32.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.e1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.E', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891224
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.P', '16.F'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': [1197, -1, 9, -1], 'generators': [122000787877207687, 51090957482037557056, 51347041223585195521, 350258752818637669031753, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.32.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.f1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.F', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891225
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.Q', '16.F'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': [2138, -1, 101, -1], 'generators': [122000787877207687, 1313941668480, 25903229683158464676480, 242140587575261560029503, 1313941673647, 51090957482037557056, 377740048764960017], 'label': '6144.ze.32.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.g1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.G', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891226
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '16.G', '16.L', '16.M'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 8, 'diagramx': [260, -1, 740, -1], 'generators': [122000787877207687, 187973563958306240457616, 108118287248261452641239, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.32.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.M', 'old_label': '32.h1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.H', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 229891227
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.R', '16.F'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': [2109, -1, 130, -1], 'generators': [122000787877207687, 350258630815053812298823, 51468697530548501041, 51347041223585195521, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.32.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.i1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.I', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 229891228
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.S', '16.F'], 'contains': [], 'core': '384.A', 'coset_action_label': None, 'count': 16, 'diagramx': [1834, -1, 30, -1], 'generators': [122000787877207687, 51090961780558017359, 54003247877598743421360, 350207661526378538814857, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.32.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.j1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.J', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 229891229
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '16.H', '16.K', '16.N', '16.O', '16.P', '16.Q', '16.R'], 'contains': ['96.A'], 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': [489, -1, 424, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942], 'label': '6144.ze.32.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.k1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.K', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891230
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.T', '16.E', '16.S'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2465, -1, 1540, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 242140587575261560029503, 1313941673647, 51091303471599669696, 108118165243376109012342], 'label': '6144.ze.32.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.l1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.L', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891231
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.T', '16.E', '16.T'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2432, -1, 1573, -1], 'generators': [187922473367523358862032, 51212595668145448193, 122010491578389112, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.32.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.m1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.M', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891232
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.T', '16.H', '16.U'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 8, 'diagramx': [2215, -1, 871, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 122003583856732942, 51091299166851820921], 'label': '6144.ze.32.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.L', 'old_label': '32.n1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.N', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891233
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.E', '4.O'], 'contains': ['16.K', '16.Q', '16.R', '16.BC', '24.ER', '32.G'], 'core': '48.C', 'coset_action_label': None, 'count': 4, 'diagramx': [723, -1, 379, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.8.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '8.q1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.Q', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891234
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.T', '16.G'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': [382, -1, 938, -1], 'generators': [187973563958306240457616, 108118287248261452641239, 51091299166851820921, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.32.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.G', 'old_label': '32.o1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.O', 'subgroup_fusion': None, 'weyl_group': '192.1008'}
  • id: 229891235
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.B', '16.I', '16.S', '16.T'], 'contains': ['128.B'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': [2560, -1, 1446, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 51091303471599669696, 108118165243376109012342, 51090957482037557056], 'label': '6144.ze.32.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.p1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.P', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891236
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.W', '16.J', '16.S', '16.T'], 'contains': ['128.C'], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': [2535, -1, 1514, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 51091303471599669696, 108118165243376109012342], 'label': '6144.ze.32.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.q1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.Q', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891349
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '512.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.H', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['128.B', '256.C', '256.E'], 'contains': ['1024.A', '1536.BB'], 'core': '3072.A', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [25903229683158464681647, 242140465572991644960126, 51090954698471793966], 'label': '6144.ze.512.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.B', 'old_label': '512.d1.NC2', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.D', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891237
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.B', '16.K', '16.U', '16.V'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 8, 'diagramx': [1986, -1, 585, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 122003583856732942, 51090954698471793966], 'label': '6144.ze.32.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.r1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.R', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891238
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.U', '16.N', '16.V'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 8, 'diagramx': [212, -1, 291, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 122003583856732942], 'label': '6144.ze.32.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.P', 'old_label': '32.s1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.S', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891239
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.V', '16.O', '16.V'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 8, 'diagramx': [158, -1, 187, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 242089496283014884627199, 51468700347165007319, 122003583856732942], 'label': '6144.ze.32.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.P', 'old_label': '32.t1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.T', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891240
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.V', '16.L'], 'contains': [], 'core': '768.A', 'coset_action_label': None, 'count': 16, 'diagramx': [35, -1, 635, -1], 'generators': [187973563958306240457616, 108118287248261452641239, 242140587575261560029503, 25903229683158464676480, 1313941673647, 1313941668480, 378111052493809927], 'label': '6144.ze.32.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.L', 'old_label': '32.u1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.U', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891241
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.W', '16.P', '16.U'], 'contains': [], 'core': '192.H', 'coset_action_label': None, 'count': 8, 'diagramx': [2302, -1, 822, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 51090961780558017359, 54003503616859417437382, 242089496283014884627199, 122003583856732942], 'label': '6144.ze.32.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.L', 'old_label': '32.v1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.V', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891242
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.C', '16.E', '16.W'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 16, 'diagramx': [2029, -1, 1359, -1], 'generators': [122000787877207687, 25903229683158464676480, 242140587575261560029503, 5606234750137, 1313941673647, 51091303471599669696, 108118165243376109012342], 'label': '6144.ze.32.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.w1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.W', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891243
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.X', '16.F'], 'contains': ['128.D'], 'core': '384.B', 'coset_action_label': None, 'count': 128, 'diagramx': [1607, -1, 78, -1], 'generators': [122000787877207687, 51090957482037557056, 51091299166851820921, 242140587575261560029503, 25903229683158464676480, 1313941673647, 377741362626794897], 'label': '6144.ze.32.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.x1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.X', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 229891244
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.F', '4.O'], 'contains': ['16.N', '16.P', '16.R', '16.BD', '24.FD', '32.I'], 'core': '48.B', 'coset_action_label': None, 'count': 4, 'diagramx': [664, -1, 410, -1], 'generators': [242140587575261560029503, 1313941668480, 25903229683158464676480, 1313941673647, 51347041223585195521, 54003503616859417437382, 4097467157062, 51468697530548501041, 122003583856732942], 'label': '6144.ze.8.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '8.r1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.R', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891245
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.C', '16.H', '16.X', '16.Y', '16.Z'], 'contains': ['96.B'], 'core': '96.B', 'coset_action_label': None, 'count': 8, 'diagramx': [433, -1, 508, -1], 'generators': [54003503616859417437382, 4097467157062, 242140587575261560029503, 25903229683158464676480, 1313941673647, 122003583856732942, 51091297865364919801], 'label': '6144.ze.32.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.y1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.Y', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891246
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.C', '16.G', '16.BA'], 'contains': [], 'core': '384.B', 'coset_action_label': None, 'count': 16, 'diagramx': [236, -1, 895, -1], 'generators': [122000787877207687, 187973563958306240457616, 108118287248261452641239, 242140587575261560029503, 25903229683158464676480, 1313941673647, 51091297865364919801], 'label': '6144.ze.32.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.M', 'old_label': '32.z1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.Z', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 229891247
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.D', '16.I', '16.W'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 16, 'diagramx': [2162, -1, 1257, -1], 'generators': [122000787877207687, 25903229683158464676480, 242140587575261560029503, 1313941673647, 51090956180549930176, 51091303471599669696, 108118165243376109012342], 'label': '6144.ze.32.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.ba1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BA', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891248
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.G', '16.J', '16.W'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 16, 'diagramx': [2058, -1, 1276, -1], 'generators': [122000787877207687, 25903229683158464676480, 242140587575261560029503, 1313941673647, 51090961780558017359, 51091303471599669696, 108118165243376109012342], 'label': '6144.ze.32.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.bb1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BB', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891249
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.D', '16.K', '16.X', '16.BB', '16.BC'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 8, 'diagramx': [518, -1, 452, -1], 'generators': [54003503616859417437382, 4097467157062, 242140587575261560029503, 25903229683158464676480, 1313941673647, 122003583856732942, 51090956180549930176], 'label': '6144.ze.32.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.bc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BC', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891250
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.F', '16.L', '16.BA'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 16, 'diagramx': [61, -1, 660, -1], 'generators': [122000787877207687, 187973563958306240457616, 108118287248261452641239, 242140587575261560029503, 25903229683158464676480, 1313941673647, 378111052493809927], 'label': '6144.ze.32.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.M', 'old_label': '32.bd1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BD', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 229891251
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.I', '16.M', '16.BA'], 'contains': [], 'core': '768.B', 'coset_action_label': None, 'count': 16, 'diagramx': [82, -1, 717, -1], 'generators': [122000787877207687, 187973563958306240457616, 51468697530548501041, 108118287248261452641239, 242140587575261560029503, 25903229683158464676480, 1313941673647], 'label': '6144.ze.32.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.L', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.M', 'old_label': '32.be1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BE', 'subgroup_fusion': None, 'weyl_group': '384.5677'}
  • id: 229891252
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.E', '16.N', '16.Y', '16.BB', '16.BD'], 'contains': ['96.C'], 'core': '96.C', 'coset_action_label': None, 'count': 8, 'diagramx': [316, -1, 317, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 51347039909644252801, 54003503616859417437382, 4097467157062, 122003583856732942], 'label': '6144.ze.32.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.K', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.bf1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BF', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891253
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.F', '16.O', '16.Z', '16.BB', '16.BE'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 8, 'diagramx': [287, -1, 238, -1], 'generators': [25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 242089496283014884627199, 51468700347165007319, 122003583856732942], 'label': '6144.ze.32.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.bg1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BG', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891254
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.G', '16.P', '16.X', '16.BD', '16.BE'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 8, 'diagramx': [460, -1, 481, -1], 'generators': [25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 242089496283014884627199, 122003583856732942], 'label': '6144.ze.32.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.bh1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BH', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891255
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.G', '4.O'], 'contains': ['16.O', '16.P', '16.Q', '16.BE', '24.FF', '32.J'], 'core': '48.C', 'coset_action_label': None, 'count': 4, 'diagramx': [602, -1, 265, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 4097467157062, 242089496283014884627199, 122003583856732942, 377740048764960017], 'label': '6144.ze.8.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '8.s1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.S', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891256
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.H', '16.Q', '16.Y', '16.BC', '16.BE'], 'contains': ['96.D'], 'core': '96.D', 'coset_action_label': None, 'count': 8, 'diagramx': [407, -1, 343, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 377740048764960017], 'label': '6144.ze.32.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.bi1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BI', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891257
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.I', '16.R', '16.Z', '16.BC', '16.BD'], 'contains': [], 'core': '192.I', 'coset_action_label': None, 'count': 8, 'diagramx': [360, -1, 371, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51468696229140707761], 'label': '6144.ze.32.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.I', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.bj1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BJ', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891258
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.Y', '16.E', '16.BF'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 16, 'diagramx': [2335, -1, 1415, -1], 'generators': [187922473367523358862032, 51212595668145448193, 122010491578389112, 122002101738316807, 242140587575261560029503, 25903229683158464676480, 1313941673647], 'label': '6144.ze.32.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.bk1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BK', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891259
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.Y', '16.G'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 16, 'diagramx': [340, -1, 915, -1], 'generators': [187973563958306240457616, 25903229683158464676480, 242140587575261560029503, 122002101738316807, 108118287248261452641239, 1313941673647, 51091299166851820921], 'label': '6144.ze.32.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.G', 'old_label': '32.bl1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BL', 'subgroup_fusion': None, 'weyl_group': '192.1008'}
  • id: 229891260
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.Y', '16.H', '16.BG'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 8, 'diagramx': [2081, -1, 795, -1], 'generators': [2796059363782, 54003503616859417437382, 51091299166851820921, 242140587575261560029503, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.32.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.L', 'old_label': '32.bm1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BM', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891261
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.J', '16.I', '16.BF'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 16, 'diagramx': [2383, -1, 1294, -1], 'generators': [122002101738316807, 25903229683158464676480, 1313941673647, 51091303471599669696, 108118165243376109012342, 216237479891421308907006, 51090954698471793966], 'label': '6144.ze.32.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.J', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.bn1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BN', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891262
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.BB', '16.J', '16.BF'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 16, 'diagramx': [2364, -1, 1387, -1], 'generators': [187922473367523358862032, 51212595668145448193, 51090961780558017359, 122002101738316807, 25903229683158464676480, 1313941673647, 216237479891421308907006], 'label': '6144.ze.32.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.bo1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BO', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891263
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.J', '16.K', '16.BG', '16.BH'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 8, 'diagramx': [1938, -1, 556, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 2796059363782, 122003583856732942, 51090957482037557056], 'label': '6144.ze.32.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '32.bp1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BP', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891264
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.BA', '16.L'], 'contains': [], 'core': '768.C', 'coset_action_label': None, 'count': 16, 'diagramx': [10, -1, 610, -1], 'generators': [187973563958306240457616, 108118287248261452641239, 122002101738316807, 242140587575261560029503, 25903229683158464676480, 1313941673647, 378111052493809927], 'label': '6144.ze.32.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.L', 'old_label': '32.bq1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BQ', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891265
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.Z', '16.N', '16.BH'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 8, 'diagramx': [186, -1, 265, -1], 'generators': [2796059363782, 54003503616859417437382, 51347041223585195521, 242140587575261560029503, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.32.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.P', 'old_label': '32.br1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BR', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891266
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '4.P'], 'contains': ['16.A', '16.BI', '24.GC', '32.L', '32.M', '32.N', '32.O'], 'core': '16.A', 'coset_action_label': None, 'count': 2, 'diagramx': [2175, -1, 1017, -1], 'generators': [6920176418617, 1313941668480, 242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.8.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '8.t1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.T', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 229891267
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.BA', '16.O', '16.BH'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 8, 'diagramx': [107, -1, 159, -1], 'generators': [2796059363782, 54003503616859417437382, 242089496283014884627199, 51468700347165007319, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.32.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.P', 'old_label': '32.bs1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BS', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891268
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.BB', '16.P', '16.BG'], 'contains': [], 'core': '192.J', 'coset_action_label': None, 'count': 8, 'diagramx': [2186, -1, 768, -1], 'generators': [2796059363782, 54003503616859417437382, 51090961780558017359, 242089496283014884627199, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.32.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.L', 'old_label': '32.bt1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BT', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891269
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.BC', '16.S', '16.W', '16.BF'], 'contains': ['128.A'], 'core': '1536.A', 'coset_action_label': None, 'count': 64, 'diagramx': [2491, -1, 1471, -1], 'generators': [5606234750137, 25903229683158464676480, 242140587575261560029503, 1313941673647, 51091303471599669696, 108118165243376109012342, 51090957482037557056], 'label': '6144.ze.32.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.bu1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BU', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891270
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.BC', '16.T', '16.W', '16.BF'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 64, 'diagramx': [2513, -1, 1493, -1], 'generators': [187922473367523358862032, 51212595668145448193, 122010491578389112, 51090954698471793966, 25903229683158464676480, 1313941673647, 216237479891421308907006], 'label': '6144.ze.32.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '32.bv1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BV', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891271
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.BC', '16.U', '16.X', '16.BG'], 'contains': [], 'core': '384.C', 'coset_action_label': None, 'count': 64, 'diagramx': [2276, -1, 848, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 122003583856732942, 51091299166851820921, 51090954698471793966], 'label': '6144.ze.32.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.L', 'old_label': '32.bw1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BW', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891272
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '32.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.BD', '16.V', '16.BB', '16.BH'], 'contains': [], 'core': '384.C', 'coset_action_label': None, 'count': 64, 'diagramx': [133, -1, 213, -1], 'generators': [25903229683158464676480, 1313941673647, 51347039909644252801, 54003503616859417437382, 242089496283014884627199, 51468700347165007319, 122003583856732942], 'label': '6144.ze.32.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.K', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.P', 'old_label': '32.bx1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.BX', 'subgroup_fusion': None, 'weyl_group': '192.956'}
  • id: 229891273
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '48.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.H', '24.A', '24.Q', '24.BD', '24.BN', '24.BO'], 'contains': ['96.A', '96.B'], 'core': '48.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6362, -1, 7547], 'generators': [54003503616859417437382, 4097467157062, 51091299166851820921, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.48.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': ['12.A', '24.A'], 'normal_contains': ['96.A', '96.B', '192.A'], 'normalizer': '1.a1', 'old_label': '48.a1.N', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.A', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 229891274
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '48.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': ['128.A'], 'conjugacy_class_count': 1, 'contained_in': ['16.N', '24.A', '24.CM', '24.DA', '24.EN', '24.FD'], 'contains': ['96.A', '96.C'], 'core': '48.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 7567, -1, 8043], 'generators': [54003503616859417437382, 4097467157062, 51347041223585195521, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.48.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': ['12.B', '24.A'], 'normal_contains': ['96.A', '96.C'], 'normalizer': '1.a1', 'old_label': '48.b1.N', 'projective_image': '2500.l', 'quotient_action_image': '48.48', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.B', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 229891275
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '48.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.C', 'complements': ['128.A'], 'conjugacy_class_count': 1, 'contained_in': ['16.Q', '24.A', '24.CQ', '24.DD', '24.ER', '24.FF'], 'contains': ['96.A', '96.D'], 'core': '48.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6965, -1, 8583], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 377740048764960017], 'label': '6144.ze.48.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.C', 'normal_contained_in': ['12.C', '24.A'], 'normal_contains': ['96.A', '96.D'], 'normalizer': '1.a1', 'old_label': '48.c1.N', 'projective_image': '2500.l', 'quotient_action_image': '48.48', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.C', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891276
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '48.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['128.D'], 'conjugacy_class_count': 1, 'contained_in': ['16.A', '24.B', '24.GC', '24.HT', '24.HU', '24.HV', '24.HW'], 'contains': ['96.E'], 'core': '48.D', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5035, -1, 3624], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.48.D', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': ['16.A', '24.B'], 'normal_contains': ['96.E', '192.H'], 'normalizer': '1.a1', 'old_label': '48.d1.N', 'projective_image': '2500.l', 'quotient_action_image': '48.38', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.D', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229891277
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.C', '4.Q'], 'contains': ['16.A', '16.BJ', '24.HU', '32.S'], 'core': '16.A', 'coset_action_label': None, 'count': 2, 'diagramx': [541, -1, 662, -1], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 377748450845332417, 1313941673647, 242140587575261560029503, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.8.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '8.u1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.U', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 229891278
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '48.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': ['128.B', '128.A', '128.C'], 'conjugacy_class_count': 4, 'contained_in': ['16.Y', '24.A', '24.IN', '24.IY', '24.JT'], 'contains': ['96.B', '96.C', '96.D'], 'core': '48.E', 'coset_action_label': None, 'count': 4, 'diagramx': [-1, 5809, -1, 7051], 'generators': [54003503616859417437382, 4097467157062, 51091299166851820921, 25903229683158464676480, 1313941673647, 122003583856732942, 377741362626794897], 'label': '6144.ze.48.E', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.E', 'normal_contained_in': ['12.D', '24.A'], 'normal_contains': ['96.B', '96.C', '96.D'], 'normalizer': '1.a1', 'old_label': '48.e1.N', 'projective_image': '6144.ze', 'quotient_action_image': '24.12', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.E', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 229891279
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '48.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.B', '24.B', '24.C', '24.D', '24.E', '24.ME', '24.MF', '24.MG', '24.MH'], 'contains': ['96.E'], 'core': '48.F', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3921, -1, 2633], 'generators': [54003503616859417437382, 4097467157062, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.48.F', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.F', 'normal_contained_in': ['16.B', '24.B', '24.C', '24.D', '24.E'], 'normal_contains': ['96.E', '192.I'], 'normalizer': '1.a1', 'old_label': '48.f1.N', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.F', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229891280
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '48.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['128.D'], 'conjugacy_class_count': 1, 'contained_in': ['16.C', '24.B', '24.NH', '24.OL', '24.OM', '24.ON', '24.OO'], 'contains': ['96.E'], 'core': '48.G', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4482, -1, 3129], 'generators': [2796059363782, 54003503616859417437382, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.48.G', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '48.G', 'normal_contained_in': ['16.C', '24.B'], 'normal_contains': ['96.E', '192.J'], 'normalizer': '1.a1', 'old_label': '48.g1.N', 'projective_image': '6144.ze', 'quotient_action_image': '48.38', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.G', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229891281
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '64.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.S'], 'contains': ['128.A', '128.B', '128.C', '256.E'], 'core': '3072.A', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [25852138754983141680143, 51091304773086575983, 6920176418617, 25903229683158464681647, 242140587575261560029503, 134021394925220632015417], 'label': '6144.ze.64.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.A', 'old_label': '64.c1.NC1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.A', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 229891282
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '64.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.F'], 'contains': ['128.D', '192.E'], 'core': '3072.A', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 25903229683158464681647, 242140587575261560029503, 51091297865364924726, 377740048764960017], 'label': '6144.ze.64.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.B', 'old_label': '64.e1.NC1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.B', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 229891283
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '96.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.C', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.K', '48.A', '48.B', '48.C'], 'contains': ['192.H', '192.I', '192.J'], 'core': '96.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 7546, -1, 8583], 'generators': [54003503616859417437382, 4097467157062, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.96.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': ['24.B', '48.A', '48.B', '48.C'], 'normal_contains': ['192.H', '192.I', '192.J', '384.A'], 'normalizer': '1.a1', 'old_label': '96.a1.N', 'projective_image': '2500.l', 'quotient_action_image': '48.48', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '96.A', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891284
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '96.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['32.Y', '48.A', '48.E'], 'contains': ['192.I'], 'core': '96.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 5809, -1, 7025], 'generators': [54003503616859417437382, 4097467157062, 25903229683158464676480, 1313941673647, 122003583856732942, 51091297865364919801], 'label': '6144.ze.96.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '96.B', 'normal_contained_in': ['24.C', '48.A', '48.E'], 'normal_contains': ['192.I', '384.B'], 'normalizer': '1.a1', 'old_label': '96.b1.N', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.B', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 229891285
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '96.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': ['64.A'], 'conjugacy_class_count': 2, 'contained_in': ['32.BF', '48.B', '48.E'], 'contains': ['192.I'], 'core': '96.C', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 6833, -1, 7643], 'generators': [54003503616859417437382, 4097467157062, 51347039909644252801, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.96.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '96.C', 'normal_contained_in': ['24.D', '48.B', '48.E'], 'normal_contains': ['192.I'], 'normalizer': '1.a1', 'old_label': '96.c1.N', 'projective_image': '6144.ze', 'quotient_action_image': '48.48', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '96.C', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 229891286
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '96.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.C', 'complements': ['64.A'], 'conjugacy_class_count': 2, 'contained_in': ['32.BI', '48.C', '48.E'], 'contains': ['192.I'], 'core': '96.D', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 6321, -1, 8102], 'generators': [54003503616859417437382, 4097467157062, 25903229683158464676480, 1313941673647, 377740048764960017, 122003583856732942], 'label': '6144.ze.96.D', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '96.D', 'normal_contained_in': ['24.E', '48.C', '48.E'], 'normal_contains': ['192.I'], 'normalizer': '1.a1', 'old_label': '96.d1.N', 'projective_image': '6144.ze', 'quotient_action_image': '48.48', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '96.D', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891287
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '96.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['64.B'], 'conjugacy_class_count': 1, 'contained_in': ['32.A', '48.D', '48.F', '48.G'], 'contains': [], 'core': '96.E', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5014, -1, 3377], 'generators': [54003503616859417437382, 51091303471599669696, 108118165243376109012342, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.96.E', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '96.E', 'normal_contained_in': ['32.A', '48.D', '48.F', '48.G'], 'normal_contains': ['384.C'], 'normalizer': '1.a1', 'old_label': '96.e1.N', 'projective_image': '6144.ze', 'quotient_action_image': '48.38', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '96.E', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229891288
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.D', '4.Q'], 'contains': ['16.A', '16.BK', '24.HV', '32.T', '32.U'], 'core': '16.A', 'coset_action_label': None, 'count': 2, 'diagramx': [377, -1, 578, -1], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 51468700347165007319, 242140587575261560029503, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.8.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '8.v1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.V', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 229891289
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '128.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.BU', '64.A'], 'contains': ['256.A', '256.B', '512.A'], 'core': '6144.a1', 'coset_action_label': None, 'count': 512, 'diagramx': None, 'generators': [25852138754983141680143, 51091304773086575983, 6920176418617, 242140587575261560029503, 134021394925220632015417], 'label': '6144.ze.128.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.A', 'old_label': '128.c1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.A', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 229891290
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '128.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.P', '64.A'], 'contains': ['256.A', '512.D'], 'core': '3072.A', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [25852138754983141680143, 25903229683158464681647, 51091303471599669696, 108118165243376109012342, 242140587575261560029503], 'label': '6144.ze.128.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.A', 'old_label': '128.e1.NC1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.B', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 229891291
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '128.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.Q', '64.A'], 'contains': ['256.B', '512.F'], 'core': '3072.A', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [51212595668145448193, 25852138759281662150272, 187922473366221951073919, 25903229683158464681647, 216237479891421308907006], 'label': '6144.ze.128.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.A', 'old_label': '128.e1.NC3', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.C', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 229891292
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '128.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.X', '64.B'], 'contains': ['384.D'], 'core': '6144.a1', 'coset_action_label': None, 'count': 512, 'diagramx': None, 'generators': [122000787877207687, 242140587575261560029503, 51091297865364924726, 377740048764960017, 51090956180549930176], 'label': '6144.ze.128.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.B', 'old_label': '128.g1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.D', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 229891293
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['384.A', '384.B'], 'core': '192.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 8532, -1, 9426], 'generators': [122000787877207687, 51091299166851820921, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.192.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': ['48.A'], 'normal_contains': ['384.A', '384.B'], 'normalizer': '1.a1', 'old_label': '192.a1.N', 'projective_image': '2500.l', 'quotient_action_image': '192.955', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '192.A', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891294
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['384.G', '384.L', '384.S', '384.V', '384.Z'], 'core': '3072.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 25903229683158464681647, 51212591375852361623, 377740048764960017], 'label': '6144.ze.192.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '192.a1.NC1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.B', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891299
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.E', '4.P'], 'contains': ['16.A', '16.BL', '24.HW', '32.Q', '32.V'], 'core': '16.A', 'coset_action_label': None, 'count': 2, 'diagramx': [2399, -1, 942, -1], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 242140587575261560029503, 108118165243376109012342, 51090961780558017359, 54003503616859417437382], 'label': '6144.ze.8.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '8.w1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.W', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 229891300
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['384.E', '384.J', '384.U', '384.Y', '384.BB'], 'core': '3072.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 25903229683158464681647, 377741362626800062, 51091297865364924726], 'label': '6144.ze.192.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '192.a1.NC6', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.G', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891301
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.C', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.A'], 'contains': ['384.C'], 'core': '192.H', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 7871, -1, 8982], 'generators': [54003503616859417437382, 25903229683158464676480, 1313941673647, 1313941668480, 122003583856732942], 'label': '6144.ze.192.H', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '192.H', 'normal_contained_in': ['48.D', '96.A'], 'normal_contains': ['384.C', '768.A'], 'normalizer': '1.a1', 'old_label': '192.b1.N', 'projective_image': '2500.l', 'quotient_action_image': '48.48', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '192.H', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891302
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.C', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.A', '96.B', '96.C', '96.D'], 'contains': ['384.C'], 'core': '192.I', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6577, -1, 7820], 'generators': [54003503616859417437382, 4097467157062, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.192.I', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '192.I', 'normal_contained_in': ['48.F', '96.A', '96.B', '96.C', '96.D'], 'normal_contains': ['384.C', '768.B'], 'normalizer': '1.a1', 'old_label': '192.c1.N', 'projective_image': '6144.ze', 'quotient_action_image': '48.48', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '192.I', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891303
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '192.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.C', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.A'], 'contains': ['384.C'], 'core': '192.J', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 7224, -1, 8401], 'generators': [2796059363782, 54003503616859417437382, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.192.J', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '192.J', 'normal_contained_in': ['48.G', '96.A'], 'normal_contains': ['384.C', '768.C'], 'normalizer': '1.a1', 'old_label': '192.d1.N', 'projective_image': '6144.ze', 'quotient_action_image': '48.48', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '192.J', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891304
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '256.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['128.A', '128.B'], 'contains': ['1024.A'], 'core': '6144.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [242140465572991644960126, 51091303471599669696, 51090954698471793966, 134021394925220632015417], 'label': '6144.ze.256.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.J', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.A', 'old_label': '256.a1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.A', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 229891305
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '256.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1536.F', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['128.A', '128.C'], 'contains': ['1024.B'], 'core': '6144.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [51212595668145448193, 51090963094498960079, 187922473366221951073919, 216237479891421308907006], 'label': '6144.ze.256.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.A', 'old_label': '256.a1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.B', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 229891306
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '256.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['512.B', '512.D', '512.H', '768.O'], 'core': '3072.A', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [324355645136098904815303, 25903229683158464681647, 51090954698471793966, 25852394838724689328686], 'label': '6144.ze.256.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '256.c1.NC1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.C', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891307
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '256.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['512.B', '512.C', '512.G', '768.P'], 'core': '6144.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [25852138754983141680143, 51347039909644257966, 25903107681056726359687, 350258752818637669031753], 'label': '6144.ze.256.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '256.c1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.D', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891308
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '256.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.A'], 'contains': ['512.A', '512.D', '512.F', '768.I'], 'core': '3072.A', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [25852138385293099761846, 25903229683158464681647, 242140465572991644960126, 51090954698471793966], 'label': '6144.ze.256.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '256.d1.NC1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.E', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891309
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '256.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['512.A', '512.C', '512.E', '768.J'], 'core': '6144.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [25903107682370587473960, 25852138385293099761846, 242140465572991644960126, 51090954698471793966], 'label': '6144.ze.256.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '256.d1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.F', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891310
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '2.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['3072.C', '3072.H', '3072.E', '3072.F', '3072.G'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.C', '4.E', '4.G', '4.M', '6.N', '8.R'], 'core': '2.F', 'coset_action_label': None, 'count': 1, 'diagramx': [711, 5864, 808, 4327], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 377748450845332417, 1313941673647, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382, 51468697530548501041], 'label': '6144.ze.2.F', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.C', '4.E', '4.G', '4.M'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '2500.l', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.F', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891311
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.H', '4.O'], 'contains': ['16.X', '16.Y', '16.Z', '16.BB', '16.BC', '16.BD', '16.BE', '24.JT', '32.X'], 'core': '48.E', 'coset_action_label': None, 'count': 32, 'diagramx': [447, -1, 345, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091297865364919801, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.8.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '8.x1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.X', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
  • id: 229891312
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.A'], 'contains': ['768.A', '768.B', '768.C'], 'core': '384.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 8700, -1, 9578], 'generators': [122000787877207687, 25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.384.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '384.A', 'normal_contained_in': ['96.A', '192.A'], 'normal_contains': ['768.A', '768.B', '768.C'], 'normalizer': '1.a1', 'old_label': '384.a1.N', 'projective_image': '2500.l', 'quotient_action_image': '24.12', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '384.A', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 229891313
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.A', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['192.A'], 'contains': ['768.B'], 'core': '384.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 8363, -1, 9275], 'generators': [122000787877207687, 51091299166851820921, 25903229683158464676480, 1313941673647], 'label': '6144.ze.384.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '384.B', 'normal_contained_in': ['96.B', '192.A'], 'normal_contains': ['768.B'], 'normalizer': '1.a1', 'old_label': '384.b1.N', 'projective_image': '6144.ze', 'quotient_action_image': '192.955', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '384.B', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 229891314
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.C', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.H', '192.I', '192.J'], 'contains': [], 'core': '384.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 7224, -1, 8401], 'generators': [54003503616859417437382, 25903229683158464676480, 1313941673647, 122003583856732942], 'label': '6144.ze.384.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '384.C', 'normal_contained_in': ['96.E', '192.H', '192.I', '192.J'], 'normal_contains': ['1536.A'], 'normalizer': '1.a1', 'old_label': '384.c1.N', 'projective_image': '6144.ze', 'quotient_action_image': '48.48', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '384.C', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 229891315
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['128.D', '192.E', '192.F'], 'contains': ['768.R', '768.W', '768.Y', '768.BB'], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 51091299166851820921, 377740048764960017], 'label': '6144.ze.384.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.c1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.D', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891316
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['192.F', '192.G'], 'contains': ['768.S', '768.X', '768.Y', '768.BB'], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 377741362626800062, 51091297865364924726], 'label': '6144.ze.384.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.c1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.E', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891317
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['192.C', '192.D'], 'contains': ['768.U', '768.X', '768.Z', '768.BA'], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [122000787877207687, 51212590061910698296, 377741362626800062, 51090956180549930176], 'label': '6144.ze.384.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.c1.NC3', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.F', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891318
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['192.B', '192.C'], 'contains': ['768.T', '768.W', '768.Z', '768.BA'], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [122000787877207687, 25852138754983141680143, 51212591375852361623, 377740048764960017], 'label': '6144.ze.384.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.c1.NC4', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.G', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891319
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.E'], 'contains': ['768.R'], 'core': '3072.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [122000787877207687, 25903229683158464681647, 51091299166851820921, 377740048764960017], 'label': '6144.ze.384.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '384.d1.NC1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.H', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891322
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '4.R'], 'contains': ['16.C', '16.BI', '24.NH', '32.BK', '32.BL', '32.BM'], 'core': '16.C', 'coset_action_label': None, 'count': 2, 'diagramx': [1874, -1, 969, -1], 'generators': [6920176418617, 25903229683158464676480, 242140587575261560029503, 1313941673647, 54003503616859417437382, 51091303471599669696, 2796059363782, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.8.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '8.y1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.Y', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 229891323
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['768.S'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 25903364133006332138897, 1313941668480, 51091297865364924726], 'label': '6144.ze.384.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC4', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.K', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891324
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.B'], 'contains': ['768.T'], 'core': '3072.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122000787877207687, 25903229683158464681647, 51212591375852361623, 377740048764960017], 'label': '6144.ze.384.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC5', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.L', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891325
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.C'], 'contains': ['768.T', '768.U'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 51212590061910698296, 25903229681844523008000, 377741362626800062], 'label': '6144.ze.384.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC6', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.M', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891326
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.D'], 'contains': ['768.U'], 'core': '3072.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [122000787877207687, 51212590061910698296, 25903229683158464681647, 377741362626800062], 'label': '6144.ze.384.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC7', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.N', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891327
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['768.T', '768.V'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [122000787877207687, 51212590061910698296, 5167, 25903364133006332138897], 'label': '6144.ze.384.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC8', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.O', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891328
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['768.V'], 'core': '3072.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 51212590061910698296, 25903229683158464681647, 25903364133006332138897], 'label': '6144.ze.384.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC9', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.P', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891329
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['768.V'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 51212590061910698296, 25903229681844523008000, 25903364133006332138897], 'label': '6144.ze.384.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC10', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.Q', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891330
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['768.U', '768.V'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [122000787877207687, 51212590061910698296, 377741362626800062, 1313941668480], 'label': '6144.ze.384.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC11', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.R', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891331
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.B', '192.E'], 'contains': ['768.W'], 'core': '3072.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138759281662150272, 25903107681056726364840, 25903229683158464681647, 79804051672210232750640], 'label': '6144.ze.384.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC16', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.S', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891332
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.C', '192.F'], 'contains': ['768.W', '768.X'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25852138759281662150272, 25903229681844523008000, 79804051673524173688447, 25903107681056726364840], 'label': '6144.ze.384.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC17', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.T', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891333
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.C', '4.S'], 'contains': ['16.C', '16.BJ', '24.OM', '32.BR'], 'core': '16.C', 'coset_action_label': None, 'count': 2, 'diagramx': [519, -1, 640, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 377748450845332417, 51091303471599669696, 2796059363782, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.8.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '8.z1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.Z', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 229891334
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.D', '192.G'], 'contains': ['768.X'], 'core': '3072.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138759281662150272, 79804051673524173688447, 25903107681056726364840, 25903229683158464681647], 'label': '6144.ze.384.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC18', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.U', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891335
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.B', '192.D'], 'contains': ['768.Z'], 'core': '3072.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 51347041223585195521, 25903229683158464681647, 25852273204830834960126], 'label': '6144.ze.384.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC19', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.V', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891336
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.C'], 'contains': ['768.Z'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122000787877207687, 25903229681844523008000, 51347041223585195521, 25852273204830834960126], 'label': '6144.ze.384.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC20', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.W', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891337
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.F'], 'contains': ['768.Y'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229681844523008000, 51468697530548501041, 25852394837410748380801, 122002101738321960], 'label': '6144.ze.384.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC21', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.X', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891338
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.E', '192.G'], 'contains': ['768.Y'], 'core': '3072.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [51468697530548501041, 25852394837410748380801, 25903229683158464681647, 122002101738321960], 'label': '6144.ze.384.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC22', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.Y', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891339
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.B', '192.D'], 'contains': ['768.BA'], 'core': '3072.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [51468697530548501041, 25903229683158464681647, 122002101738321960, 25852017097362197157143], 'label': '6144.ze.384.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC23', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.Z', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891340
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.C'], 'contains': ['768.BA'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229681844523008000, 51468697530548501041, 122002101738321960, 25852017097362197157143], 'label': '6144.ze.384.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC24', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BA', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891341
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.E', '192.G'], 'contains': ['768.BB'], 'core': '3072.A', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [51468697530548501041, 25903229683158464681647, 122002101738321960, 25852138383991612855801], 'label': '6144.ze.384.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC25', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BB', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891342
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.F'], 'contains': ['768.BB'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229681844523008000, 51468697530548501041, 122002101738321960, 25852138383991612855801], 'label': '6144.ze.384.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC26', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BC', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891343
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['768.BC'], 'core': '3072.A', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [134021394932128353619200, 25903229683158464681647, 187973307875878553928360, 79855520717031869819393], 'label': '6144.ze.384.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC27', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BD', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891344
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.D', '4.S'], 'contains': ['16.C', '16.BK', '24.ON', '32.BQ', '32.BS'], 'core': '16.C', 'coset_action_label': None, 'count': 2, 'diagramx': [355, -1, 556, -1], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941673647, 51468700347165007319, 242140587575261560029503, 2796059363782, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.8.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '8.ba1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.BA', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 229891345
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '384.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['768.BC'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [134021394932128353619200, 25903229681844523008000, 187973307875878553928360, 79855520717031869819393], 'label': '6144.ze.384.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '384.d1.NC28', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.BE', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891346
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '512.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['128.A', '256.E', '256.F'], 'contains': ['1024.A', '1024.B', '1536.X'], 'core': '6144.a1', 'coset_action_label': None, 'count': 1024, 'diagramx': None, 'generators': [25852138754983141680143, 25852138385293099756921, 242140587575261560029503], 'label': '6144.ze.512.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '512.c1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.A', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891347
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '512.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['256.C', '256.D'], 'contains': ['1024.A', '1024.C', '1536.BD'], 'core': '6144.a1', 'coset_action_label': None, 'count': 1024, 'diagramx': None, 'generators': [324355645136098904815303, 51090954698471793966, 25852394838724689328686], 'label': '6144.ze.512.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '512.c1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.B', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891354
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['384.A'], 'contains': ['1536.A'], 'core': '768.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 9038, -1, 9881], 'generators': [25903229683158464676480, 1313941673647, 1313941668480], 'label': '6144.ze.768.A', 'mobius_quo': 1, 'mobius_sub': None, 'normal_closure': '768.A', 'normal_contained_in': ['192.H', '384.A'], 'normal_contains': ['1536.A', '3072.A'], 'normalizer': '1.a1', 'old_label': '768.a1.N', 'projective_image': '2500.l', 'quotient_action_image': '6.1', 'quotient_action_kernel': '128.1578', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '768.A', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891355
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.E', '4.R'], 'contains': ['16.C', '16.BL', '24.OO', '32.BO', '32.BT'], 'core': '16.C', 'coset_action_label': None, 'count': 2, 'diagramx': [2370, -1, 916, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 51090961780558017359, 54003503616859417437382, 51091303471599669696, 2796059363782, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.8.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '8.bb1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.BB', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 229891356
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['384.A', '384.B'], 'contains': ['1536.A'], 'core': '768.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 8363, -1, 9275], 'generators': [122000787877207687, 25903229683158464676480, 1313941673647], 'label': '6144.ze.768.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '768.B', 'normal_contained_in': ['192.I', '384.A', '384.B'], 'normal_contains': ['1536.A'], 'normalizer': '1.a1', 'old_label': '768.b1.N', 'projective_image': '6144.ze', 'quotient_action_image': '24.12', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '768.B', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 229891357
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['384.A'], 'contains': ['1536.A'], 'core': '768.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 8700, -1, 9578], 'generators': [122002101738316807, 25903229683158464676480, 1313941673647], 'label': '6144.ze.768.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '768.C', 'normal_contained_in': ['192.J', '384.A'], 'normal_contains': ['1536.A'], 'normalizer': '1.a1', 'old_label': '768.c1.N', 'projective_image': '6144.ze', 'quotient_action_image': '24.12', 'quotient_action_kernel': '32.46', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '768.C', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 229891358
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['1536.E', '1536.M', '1536.W', '1536.BA'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25903229687450757758137, 25903229681844523008000, 51090954698471793966], 'label': '6144.ze.768.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.D', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891359
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['1536.D', '1536.N', '1536.W', '1536.BB'], 'core': '3072.A', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25903229687450757758137, 25903229683158464681647, 51090954698471793966], 'label': '6144.ze.768.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC2', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.E', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891360
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': [], 'contains': ['1536.B', '1536.R', '1536.W', '1536.X', '1536.BC'], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [25852138754983141680143, 25852138389597847605696, 6920176418617], 'label': '6144.ze.768.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC3', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.F', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891361
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': [], 'contains': ['1536.B', '1536.Q', '1536.W', '1536.Y', '1536.BC'], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [51090954698471793966, 25852017102968431912193, 25852017097362197157143], 'label': '6144.ze.768.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC4', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.G', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891362
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['1536.E', '1536.G', '1536.X', '1536.BA'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25903229681844523008000, 51090954698471793966, 25852138383991612855801], 'label': '6144.ze.768.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC5', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.H', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891363
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['256.E'], 'contains': ['1536.D', '1536.F', '1536.X', '1536.BB'], 'core': '3072.A', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25903229683158464681647, 51090954698471793966, 25852138383991612855801], 'label': '6144.ze.768.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC6', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.I', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891364
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['256.F'], 'contains': ['1536.C', '1536.K', '1536.X', '1536.Z'], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [25903107681056726359687, 51090954698471793966, 25852138383991612855801], 'label': '6144.ze.768.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC7', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.J', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891365
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['1536.E', '1536.H', '1536.Y', '1536.BA'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25903229681844523008000, 51090954698471793966, 25852017097362197157143], 'label': '6144.ze.768.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC8', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.K', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891366
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.H', '4.P', '4.R'], 'contains': ['16.D', '16.BI', '16.BL', '24.PE', '32.BU', '32.BV', '32.BW'], 'core': '16.D', 'coset_action_label': None, 'count': 16, 'diagramx': [2421, -1, 991, -1], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941673647, 5606234750137, 51090957482037557056, 242140587575261560029503, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.8.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '8.bc1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.BC', 'subgroup_fusion': None, 'weyl_group': '1536.408640541'}
  • id: 229891367
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['1536.D', '1536.I', '1536.Y', '1536.BB'], 'core': '3072.A', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25852138754983141680143, 25903229683158464681647, 51212591375852361623], 'label': '6144.ze.768.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC9', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.L', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891368
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['1536.C', '1536.L', '1536.Y', '1536.Z'], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [25903107681056726359687, 51090954698471793966, 25852017097362197157143], 'label': '6144.ze.768.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC10', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.M', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891369
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['1536.BA', '1536.BD', '1536.BF', '1536.BJ'], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [25903229681844523008000, 25852394837410748380801, 51090954698471793966], 'label': '6144.ze.768.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC11', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.N', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891370
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['256.C'], 'contains': ['1536.BB', '1536.BD', '1536.BG', '1536.BI'], 'core': '3072.A', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [25852394837410748380801, 25903229683158464681647, 51090954698471793966], 'label': '6144.ze.768.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC12', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.O', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891371
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['256.D'], 'contains': ['1536.Z', '1536.BD', '1536.BE', '1536.BK'], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [25903107681056726359687, 25852394837410748380801, 51090954698471793966], 'label': '6144.ze.768.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC13', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.P', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891372
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['1536.Z', '1536.BD', '1536.BE', '1536.BL'], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [25903107682370587473960, 25852138754983141680143, 51347041223585195521], 'label': '6144.ze.768.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.h1.NC14', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.Q', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891373
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.D', '384.H', '384.I'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [122000787877207687, 25903364133006332144062, 51469037914129884743], 'label': '6144.ze.768.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '768.j1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.R', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891374
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.E', '384.I', '384.J', '384.K'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [122000787877207687, 25903364133006332138897, 51091297865364924726], 'label': '6144.ze.768.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.S', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891375
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.G', '384.L', '384.M', '384.O'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [122000787877207687, 51212591375852361623, 377740048764960017], 'label': '6144.ze.768.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC3', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.T', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891376
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '768.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['384.F', '384.M', '384.N', '384.R'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [122000787877207687, 377741362626800062, 51212591375852366776], 'label': '6144.ze.768.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '768.j1.NC4', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.U', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 229891377
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '8.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.K', '4.Q', '4.S'], 'contains': ['16.D', '16.BJ', '16.BK', '24.PO', '32.BX'], 'core': '16.D', 'coset_action_label': None, 'count': 16, 'diagramx': [468, -1, 598, -1], 'generators': [242140587575261560029503, 25903229683158464676480, 1313941673647, 54003503616859417437382, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090954698471793966], 'label': '6144.ze.8.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '8.bd1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.BD', 'subgroup_fusion': None, 'weyl_group': '1536.408550734'}
  • id: 229891386
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1024.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.H', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['256.A', '512.A', '512.B', '512.C', '512.D'], 'contains': ['2048.a1', '3072.C'], 'core': '6144.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [25852138754983141680143, 242140587575261560029503], 'label': '6144.ze.1024.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.B', 'old_label': '1024.a1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1024.A', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891387
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1024.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['256.B', '512.A', '512.E', '512.F'], 'contains': ['2048.a1', '3072.D'], 'core': '6144.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [51090963094498960079, 216288449198190123592319], 'label': '6144.ze.1024.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1024.a1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1024.B', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891388
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['512.B'], 'conjugacy_class_count': 1, 'contained_in': ['4.A', '6.A', '6.F', '6.G'], 'contains': ['24.B', '24.C', '24.Q', '24.R', '24.X', '24.BU', '24.CT', '24.CU', '24.FQ', '24.FY', '24.FZ', '24.GC', '24.GE', '24.JL', '24.JM', '24.JN', '24.NE', '24.NF', '24.NG', '24.NH'], 'core': '12.A', 'coset_action_label': None, 'count': 1, 'diagramx': [2617, 1876, 2845, 2385], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.12.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': ['4.A', '6.A'], 'normal_contains': ['24.B', '24.C', '48.A'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '2500.l', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.A', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229891389
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1024.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['512.B', '512.G', '512.H'], 'contains': ['2048.a1', '3072.H'], 'core': '6144.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [242089374992119825754737, 53952156953721766679632], 'label': '6144.ze.1024.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1024.a1.NC3', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1024.C', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891390
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.A', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['768.A', '768.B', '768.C'], 'contains': [], 'core': '1536.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 8700, -1, 9578], 'generators': [25903229683158464676480, 1313941673647], 'label': '6144.ze.1536.A', 'mobius_quo': -1, 'mobius_sub': None, 'normal_closure': '1536.A', 'normal_contained_in': ['384.C', '768.A', '768.B', '768.C'], 'normal_contains': ['6144.a1'], 'normalizer': '1.a1', 'old_label': '1536.a1.N', 'projective_image': '6144.ze', 'quotient_action_image': '6.1', 'quotient_action_kernel': '256.29598', 'quotient_action_kernel_order': 256, 'quotient_fusion': None, 'short_label': '1536.A', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 229891391
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['768.F', '768.G'], 'contains': ['3072.D', '3072.K'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25852138759281662150272, 25852017102968431912193], 'label': '6144.ze.1536.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.j1.NC8', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.B', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891392
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['512.E', '768.J', '768.M'], 'contains': ['3072.D', '3072.J'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25852138759281662150272, 122002101738316807], 'label': '6144.ze.1536.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.j1.NC9', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.C', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891393
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['512.F', '768.E', '768.I', '768.L'], 'contains': ['3072.A', '3072.D'], 'core': '3072.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138759281662150272, 25903229683158464681647], 'label': '6144.ze.1536.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.j1.NC10', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.D', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891394
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.D', '768.H', '768.K'], 'contains': ['3072.D', '3072.I'], 'core': '6144.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25852138759281662150272, 25903229681844523008000], 'label': '6144.ze.1536.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.j1.NC11', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.E', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891395
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.K', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.I'], 'contains': ['3072.A', '3072.E'], 'core': '3072.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25903229683158464681647, 51091299166851820921], 'label': '6144.ze.1536.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '1536.m1.NC1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.F', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891396
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.W', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.H'], 'contains': ['3072.E', '3072.I'], 'core': '6144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51091299166851820921, 1313941668480], 'label': '6144.ze.1536.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.W', 'old_label': '1536.m1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.G', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891397
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.CS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.K'], 'contains': ['3072.F', '3072.I'], 'core': '6144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229681844523008000, 51212591375852361623], 'label': '6144.ze.1536.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CS', 'old_label': '1536.m1.NC3', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.H', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891398
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.CS', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.L'], 'contains': ['3072.A', '3072.F'], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229683158464681647, 51212591375852361623], 'label': '6144.ze.1536.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CS', 'old_label': '1536.m1.NC4', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.I', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891399
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['512.A'], 'conjugacy_class_count': 1, 'contained_in': ['4.C', '6.A', '6.L', '6.N'], 'contains': ['24.B', '24.D', '24.DA', '24.DI', '24.HK', '24.HU', '24.LI', '24.OB', '24.OM'], 'core': '12.B', 'coset_action_label': None, 'count': 1, 'diagramx': [1950, 3698, 1903, 1075], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503616859417437382, 4097467157062, 377748450845332417, 51091303471599669696, 108118165243376109012342, 122003583856732942], 'label': '6144.ze.12.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': ['4.C', '6.A'], 'normal_contains': ['24.B', '24.D', '48.B'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '2500.l', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.B', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229891400
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['3072.F', '3072.I'], 'core': '6144.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1313941668480, 51212591375852361623], 'label': '6144.ze.1536.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC5', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.J', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891401
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.J'], 'contains': ['3072.E', '3072.J'], 'core': '6144.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [122002101738316807, 51091299166851820921], 'label': '6144.ze.1536.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.B', 'old_label': '1536.m1.NC6', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.K', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891402
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.M'], 'contains': ['3072.F', '3072.J'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122002101738316807, 51212591375852361623], 'label': '6144.ze.1536.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC7', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.L', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891403
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.CH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['768.D'], 'contains': ['3072.G', '3072.I'], 'core': '6144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [25903229687450757758137, 25903229681844523008000], 'label': '6144.ze.1536.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CH', 'old_label': '1536.m1.NC8', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.M', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891404
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.CH', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['768.E'], 'contains': ['3072.A', '3072.G'], 'core': '3072.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6920176418617, 25903229683158464681647], 'label': '6144.ze.1536.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CH', 'old_label': '1536.m1.NC9', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.N', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891405
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.GE', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['3072.G', '3072.I'], 'core': '6144.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229687450757758137, 1313941668480], 'label': '6144.ze.1536.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GE', 'old_label': '1536.m1.NC10', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.O', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891406
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': [], 'contains': ['3072.F', '3072.G', '3072.L'], 'core': '6144.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [162121668863019131738742, 51212591375852361623], 'label': '6144.ze.1536.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC11', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.P', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891407
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['768.G'], 'contains': ['3072.F', '3072.G', '3072.K'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [51212591375852361623, 25852017102968431912193], 'label': '6144.ze.1536.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC12', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.Q', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891408
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['768.F'], 'contains': ['3072.E', '3072.G', '3072.K'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25852138389597847605696, 51091299166851820921], 'label': '6144.ze.1536.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC13', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.R', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891409
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['3072.G', '3072.L'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229687450757758137, 187922473370319418197817], 'label': '6144.ze.1536.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC14', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.S', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891410
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['512.A', '512.B'], 'conjugacy_class_count': 1, 'contained_in': ['4.F', '6.A', '6.M', '6.O'], 'contains': ['24.B', '24.E', '24.DD', '24.DJ', '24.LL'], 'core': '12.C', 'coset_action_label': None, 'count': 1, 'diagramx': [5024, 2763, 5657, 1730], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342, 377740048764960017], 'label': '6144.ze.12.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': ['4.F', '6.A'], 'normal_contains': ['24.B', '24.E', '48.C'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '2500.l', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.C', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229891411
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['3072.G', '3072.L'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [187922473369005476534262, 25903229687450757758137], 'label': '6144.ze.1536.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC15', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.T', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891412
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['3072.G', '3072.K'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229687450757758137, 108118165243376109007417], 'label': '6144.ze.1536.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC16', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.U', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891413
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': [], 'contains': ['3072.G', '3072.K'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903229687450757758137, 108118165244677595913462], 'label': '6144.ze.1536.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC17', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.V', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891414
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['768.D', '768.E', '768.F', '768.G'], 'contains': ['3072.C', '3072.D', '3072.G'], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [25903229687450757758137, 51090954698471793966], 'label': '6144.ze.1536.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC18', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.W', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891415
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['512.A', '768.F', '768.H', '768.I', '768.J'], 'contains': ['3072.C', '3072.D', '3072.E'], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [51090954698471793966, 25852138383991612855801], 'label': '6144.ze.1536.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC19', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.X', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891416
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['768.G', '768.K', '768.L', '768.M'], 'contains': ['3072.C', '3072.D', '3072.F'], 'core': '6144.a1', 'coset_action_label': None, 'count': 768, 'diagramx': None, 'generators': [25852138754983141680143, 51212591375852361623], 'label': '6144.ze.1536.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC20', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.Y', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891417
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['512.C', '768.J', '768.M', '768.P', '768.Q'], 'contains': ['3072.C', '3072.J'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [25903107681056726359687, 51090954698471793966], 'label': '6144.ze.1536.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.J', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC21', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.Z', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891418
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.G', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['768.D', '768.H', '768.K', '768.N'], 'contains': ['3072.C', '3072.I'], 'core': '6144.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229681844523008000, 51090954698471793966], 'label': '6144.ze.1536.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.G', 'old_label': '1536.m1.NC22', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BA', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891419
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.G', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['512.D', '768.E', '768.I', '768.L', '768.O'], 'contains': ['3072.A', '3072.C'], 'core': '3072.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229683158464681647, 51090954698471793966], 'label': '6144.ze.1536.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.G', 'old_label': '1536.m1.NC23', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BB', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891420
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['768.F', '768.G'], 'contains': ['3072.C', '3072.K'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [25852138754983141680143, 25852138389597847605696], 'label': '6144.ze.1536.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC24', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BC', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891421
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '2.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['3072.C', '3072.E', '3072.F', '3072.B', '3072.G'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.D', '4.E', '4.F', '4.N', '6.O', '8.S'], 'core': '2.G', 'coset_action_label': None, 'count': 1, 'diagramx': [685, 3571, 703, 3610], 'generators': [51091303471599669696, 25903229683158464676480, 122003583856732942, 1313941668480, 1313941673647, 377740048764960017, 242140587575261560029503, 4097467157062, 108118165243376109012342, 51090961780558017359, 54003503616859417437382], 'label': '6144.ze.2.G', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.G', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.D', '4.E', '4.F', '4.N'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': '2500.l', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.G', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891422
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': ['512.C', '512.D', '512.A', '512.B', '512.E', '512.F', '512.G', '512.H'], 'conjugacy_class_count': 4, 'contained_in': ['4.I', '6.A', '6.Q'], 'contains': ['24.C', '24.D', '24.E', '24.IN', '24.IR', '24.KN', '24.KQ'], 'core': '12.D', 'coset_action_label': None, 'count': 4, 'diagramx': [4963, 1146, 5537, 420], 'generators': [6920176418617, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342, 377740048764960017], 'label': '6144.ze.12.D', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '12.D', 'normal_contained_in': ['4.I', '6.A'], 'normal_contains': ['24.C', '24.D', '24.E', '48.E'], 'normalizer': '1.a1', 'old_label': '12.d1', 'projective_image': '6144.ze', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.D', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 229891423
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['512.B', '768.N', '768.O', '768.P', '768.Q'], 'contains': ['3072.B', '3072.C', '3072.H'], 'core': '6144.a1', 'coset_action_label': None, 'count': 1536, 'diagramx': None, 'generators': [25852138754983141680143, 51347041223585195521], 'label': '6144.ze.1536.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC25', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BD', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891424
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['512.G', '768.P', '768.Q'], 'contains': ['3072.H', '3072.J'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [122002101738316807, 53952156953721766679632], 'label': '6144.ze.1536.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC26', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BE', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891425
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.N'], 'contains': ['3072.H', '3072.I'], 'core': '6144.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229681844523008000, 53952156953721766679632], 'label': '6144.ze.1536.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC27', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BF', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891426
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['512.H', '768.O'], 'contains': ['3072.A', '3072.H'], 'core': '3072.A', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [25903229683158464681647, 53952156953721766679632], 'label': '6144.ze.1536.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC28', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BG', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891427
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['3072.H', '3072.L'], 'core': '6144.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [53952413038771203521263, 53952156953721766679632], 'label': '6144.ze.1536.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.m1.NC29', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BH', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891428
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.O'], 'contains': ['3072.A', '3072.B'], 'core': '3072.A', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [51347041223585195521, 25903229683158464681647], 'label': '6144.ze.1536.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.F', 'old_label': '1536.n1.NC8', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BI', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891429
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.N'], 'contains': ['3072.B', '3072.I'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [51347041223585195521, 1313941668480], 'label': '6144.ze.1536.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.n1.NC9', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BJ', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891430
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.P'], 'contains': ['3072.B', '3072.J'], 'core': '6144.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [25903107681056726359687, 51347041223585195521], 'label': '6144.ze.1536.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.F', 'old_label': '1536.n1.NC10', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BK', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891431
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '1536.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['768.Q'], 'contains': ['3072.B', '3072.J'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [51347041223585195521, 122002101738316807], 'label': '6144.ze.1536.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1536.n1.NC11', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1536.BL', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891432
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '2048.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1024.A', '1024.B', '1024.C'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [242140587575261560029503], 'label': '6144.ze.2048.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.B', 'old_label': '2048.a1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2048.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 229891433
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.C', '6.F'], 'contains': ['24.O', '24.Q', '24.V', '24.Y', '24.BD', '24.BV', '24.CA', '24.CV', '24.CW', '24.DC', '24.DR', '24.FK', '24.FL', '24.FS', '24.FT', '24.ID', '24.IF', '24.IS', '24.IU', '24.MS', '24.MT', '24.MW', '24.MX'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6780, -1, 6809, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.e1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.E', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891434
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['2.H'], 'conjugacy_class_count': 1, 'contained_in': ['1536.D', '1536.F', '1536.I', '1536.N', '1536.BB', '1536.BG', '1536.BI'], 'contains': ['6144.a1'], 'core': '3072.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 9629, -1, 8202], 'generators': [25903229683158464681647], 'label': '6144.ze.3072.A', 'mobius_quo': -1, 'mobius_sub': None, 'normal_closure': '3072.A', 'normal_contained_in': ['768.A'], 'normal_contains': ['6144.a1'], 'normalizer': '1.a1', 'old_label': '3072.a1.N', 'projective_image': '2500.l', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4000.fd', 'quotient_action_kernel_order': 3072, 'quotient_fusion': None, 'short_label': '3072.A', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891435
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.F', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1536.BD', '1536.BI', '1536.BJ', '1536.BK', '1536.BL'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [51347039909644252801], 'label': '6144.ze.3072.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.F', 'old_label': '3072.c1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.B', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891436
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.G', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1024.A', '1536.W', '1536.X', '1536.Y', '1536.Z', '1536.BA', '1536.BB', '1536.BC', '1536.BD'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [51090956180549930176], 'label': '6144.ze.3072.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.J', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.G', 'old_label': '3072.c1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.C', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891437
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1024.B', '1536.B', '1536.C', '1536.D', '1536.E', '1536.W', '1536.X', '1536.Y'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [51090963094498960079], 'label': '6144.ze.3072.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '3072.c1.NC3', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.D', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891438
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.K', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1536.F', '1536.G', '1536.K', '1536.R', '1536.X'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [51091297865364919801], 'label': '6144.ze.3072.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '3072.e1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.E', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891439
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.CS', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1536.H', '1536.I', '1536.J', '1536.L', '1536.P', '1536.Q', '1536.Y'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [51212591375852361623], 'label': '6144.ze.3072.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CS', 'old_label': '3072.e1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.F', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891440
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.CH', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1536.M', '1536.N', '1536.O', '1536.P', '1536.Q', '1536.R', '1536.S', '1536.T', '1536.U', '1536.V', '1536.W'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [6920176418617], 'label': '6144.ze.3072.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.CH', 'old_label': '3072.e1.NC4', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.G', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891441
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1024.C', '1536.BD', '1536.BE', '1536.BF', '1536.BG', '1536.BH'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [53952156953721766679632], 'label': '6144.ze.3072.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '3072.e1.NC6', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.H', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891442
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1536.E', '1536.G', '1536.H', '1536.J', '1536.M', '1536.O', '1536.BA', '1536.BF', '1536.BJ'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1313941668480], 'label': '6144.ze.3072.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '768.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3072.h1.NC1', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.I', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891443
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.O', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1536.C', '1536.K', '1536.L', '1536.Z', '1536.BE', '1536.BK', '1536.BL'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [122002101738316807], 'label': '6144.ze.3072.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '768.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.O', 'old_label': '3072.h1.NC2', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.J', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891444
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.F', '24.G', '24.H', '24.I', '24.O', '24.S', '24.T', '24.Z', '24.BA', '24.BB', '24.BC', '24.BW', '24.BX', '24.BY', '24.BZ', '24.CX', '24.CY', '24.DU', '24.DW', '24.IB', '24.IE', '24.IT'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8385, -1, 9689, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 4097467157062, 51091303471599669696, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.12.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.f1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.F', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891445
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.GD', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1536.B', '1536.Q', '1536.R', '1536.U', '1536.V', '1536.BC'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [51091304773086570816], 'label': '6144.ze.3072.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GD', 'old_label': '3072.h1.NC7', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.K', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891446
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '3072.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.GU', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1536.P', '1536.S', '1536.T', '1536.BH'], 'contains': ['6144.a1'], 'core': '6144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [108118165247473575438719], 'label': '6144.ze.3072.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.GU', 'old_label': '3072.h1.NC8', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3072.L', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891447
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '6144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2048.a1', '3072.A', '3072.B', '3072.C', '3072.D', '3072.E', '3072.F', '3072.G', '3072.H', '3072.I', '3072.J', '3072.K', '3072.L'], 'contains': [], 'core': '6144.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 9629, -1, 8202], 'generators': [], 'label': '6144.ze.6144.a1', 'mobius_quo': 1, 'mobius_sub': None, 'normal_closure': '6144.a1', 'normal_contained_in': ['1536.A', '3072.A'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6144.a1.N', 'projective_image': '6144.ze', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6144.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 229891448
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.A', '6.B', '6.D'], 'contains': ['24.A', '24.Q', '24.S', '24.BE', '24.BO', '24.CB', '24.CM', '24.CQ', '24.DA', '24.DD', '24.DP', '24.IG', '24.IN', '24.IY', '24.JC'], 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7121, -1, 7440, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.12.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.g1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.G', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229891449
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B', '6.E', '6.G'], 'contains': ['24.Q', '24.T', '24.BF', '24.BH', '24.BN', '24.CC', '24.CD', '24.CO', '24.DB', '24.DF', '24.DQ', '24.IH', '24.IO', '24.IZ', '24.JD'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6679, -1, 7160, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51468697530548501041, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.h1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.H', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891450
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.E', '6.F'], 'contains': ['24.Q', '24.U', '24.DE', '24.DG', '24.DS', '24.FN', '24.FO', '24.II', '24.IP', '24.MU', '24.MV'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5155, -1, 5132, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 108169256206464380536342, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.i1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.I', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891451
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.C', '6.D', '6.G'], 'contains': ['24.Q', '24.BG', '24.CE', '24.DH', '24.DK', '24.IQ', '24.JE'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5133, -1, 5089, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 108169633946512931760000, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.j1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.J', 'subgroup_fusion': None, 'weyl_group': '512.406983'}
  • id: 229891452
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '768.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.A', '6.C', '6.E'], 'contains': ['24.Q', '24.BO', '24.CR', '24.DI', '24.DJ', '24.IR', '24.JA'], 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5948, -1, 5962, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 108118542983424833692672, 54003503616859417437382, 4097467157062, 51091303471599669696, 122003583856732942], 'label': '6144.ze.12.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.k1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.K', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 229891453
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G'], 'contains': ['24.P', '24.R', '24.BF', '24.BG', '24.BI', '24.CF', '24.CG', '24.CJ', '24.CZ', '24.DL', '24.DM', '24.IJ', '24.IK', '24.IV', '24.IW'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1639, -1, 1957, -1], 'generators': [25903229683158464676480, 51091299166851820921, 122003583856732942, 1313941668480, 1313941673647, 53952413034673736392198, 4097467157062, 108118165243376109012342, 51468697530548501041], 'label': '6144.ze.12.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '12.l1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.L', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891454
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.G'], 'contains': ['24.R', '24.BG', '24.BH', '24.CH', '24.CI', '24.DN', '24.DO', '24.IL', '24.IX'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1387, -1, 2432, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 4097467157062, 256115864664974016, 53952413034673736392198, 122003583856732942, 108118165243376109012342, 51091299166851820921], 'label': '6144.ze.12.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '12.m1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.M', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 229891455
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '2.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3072.A', 'complements': ['3072.A', '3072.I', '3072.J', '3072.E', '3072.F', '3072.B', '3072.G', '3072.K', '3072.L', '3072.C', '3072.D', '3072.H'], 'conjugacy_class_count': 8, 'contained_in': ['1.a1'], 'contains': ['4.H', '4.I', '4.J', '4.K', '4.L', '4.M', '4.N', '6.Q', '8.X'], 'core': '2.H', 'coset_action_label': None, 'count': 8, 'diagramx': [659, 4379, 757, 5660], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941673647, 377740048764960017, 51090957482037557056, 242140587575261560029503, 4097467157062, 108118165243376109012342, 54003503616859417437382], 'label': '6144.ze.2.H', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.H', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.H', '4.I', '4.J', '4.K', '4.L', '4.M', '4.N'], 'normalizer': '1.a1', 'old_label': '2.h1', 'projective_image': '6144.ze', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.H', 'subgroup_fusion': None, 'weyl_group': '2500.l'}
  • id: 229891456
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.S', '24.T', '24.V', '24.BJ', '24.BK', '24.BL', '24.BM', '24.CK', '24.CL', '24.CN', '24.CP', '24.DT', '24.DV', '24.DX', '24.DY', '24.IM', '24.JB'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8625, -1, 9329, -1], 'generators': [6920176418617, 1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 4097467157062, 51091303471599669696, 122003583856732942, 377740048764960017], 'label': '6144.ze.12.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.n1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.N', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891457
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F'], 'contains': ['24.N', '24.O', '24.U', '24.W', '24.X', '24.BP', '24.BQ', '24.BR', '24.CS', '24.DZ', '24.EA', '24.FJ', '24.FP', '24.FU', '24.FV', '24.FW', '24.GA', '24.GD', '24.GF', '24.JF', '24.JG', '24.JI', '24.JJ', '24.MY', '24.MZ', '24.NB', '24.NC'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4705, -1, 4834, -1], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 51090957482037557056, 4097467157062, 108118165243376109012342], 'label': '6144.ze.12.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.o1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.O', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891458
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F'], 'contains': ['24.U', '24.V', '24.X', '24.BS', '24.BT', '24.EB', '24.EC', '24.FM', '24.FR', '24.FX', '24.GB', '24.JH', '24.JK', '24.NA', '24.ND'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3929, -1, 3460, -1], 'generators': [51091303471599669696, 25903229683158464676480, 6920176418617, 53952412685900568952456, 122003583856732942, 1313941668480, 1313941673647, 4097467157062, 108118165243376109012342], 'label': '6144.ze.12.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.p1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.P', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891459
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.Y', '24.Z', '24.BB', '24.BE', '24.BF', '24.BJ', '24.BL', '24.ED', '24.EF', '24.EL', '24.EO', '24.ET', '24.EV', '24.FB', '24.FE', '24.JO', '24.JQ'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9488, -1, 9173, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 53952413034673736392198, 122003583856732942, 51090957482037557056, 377740048764960017], 'label': '6144.ze.12.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.q1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Q', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891460
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.Y', '24.BA', '24.BC', '24.BE', '24.BH', '24.BK', '24.BM', '24.EE', '24.EG', '24.EM', '24.EQ', '24.EU', '24.EW', '24.FC', '24.FH', '24.JP', '24.JR'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8771, -1, 8516, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 53952413034673736392198, 122003583856732942, 51090957482037557056, 54003247877598743421360], 'label': '6144.ze.12.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.r1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.R', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891461
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.O', '6.B'], 'contains': ['24.A', '24.Z', '24.BA', '24.BD', '24.BJ', '24.BK', '24.BN', '24.EH', '24.EI', '24.EN', '24.ER', '24.EX', '24.EY', '24.FD', '24.FF', '24.JS', '24.JT'], 'core': '24.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7517, -1, 7984, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 122003583856732942, 51090957482037557056, 377740048764960017, 51091299166851820921], 'label': '6144.ze.12.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.s1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.S', 'subgroup_fusion': None, 'weyl_group': '128.2216'}
  • id: 229891462
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.BB', '24.BC', '24.BD', '24.BL', '24.BM', '24.BN', '24.BO', '24.EJ', '24.EK', '24.EP', '24.ES', '24.EZ', '24.FA', '24.FG', '24.FI', '24.JU', '24.JV'], 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9425, -1, 8885, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 54003503616859417437382, 4097467157062, 51347042732487422033, 122003583856732942, 51090957482037557056, 51091299166851820921], 'label': '6144.ze.12.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.t1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.T', 'subgroup_fusion': None, 'weyl_group': '256.51978'}
  • id: 229891463
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F'], 'contains': ['24.BQ', '24.BT', '24.BU', '24.CW', '24.DS', '24.DZ', '24.EB', '24.GG', '24.GK', '24.GV', '24.HQ', '24.JW', '24.JY', '24.NI', '24.NK'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4137, -1, 3629, -1], 'generators': [25903229683158464676480, 1313941668480, 1313941673647, 54003503622465652187519, 4097467157062, 51091303471599669696, 108118165243376109012342, 122003583856732942, 51090957482037557056], 'label': '6144.ze.12.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.u1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.U', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891464
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.F'], 'contains': ['24.BR', '24.BS', '24.BU', '24.DR', '24.DS', '24.EA', '24.EC', '24.GI', '24.GL', '24.HC', '24.HS', '24.JX', '24.JZ', '24.NJ', '24.NL'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3374, -1, 4142, -1], 'generators': [1313941668480, 25903229683158464676480, 1313941673647, 53952412685900568952456, 54003503622465652187519, 4097467157062, 51091303471599669696, 122003583856732942, 108118165243376109012342], 'label': '6144.ze.12.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.v1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.V', 'subgroup_fusion': None, 'weyl_group': '256.53380'}
  • id: 229891465
    {'ambient': '6144.ze', 'aut_centralizer_order': None, 'aut_label': '12.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.J', '24.K', '24.L', '24.M', '24.BV', '24.BW', '24.BY', '24.CB', '24.CC', '24.CK', '24.CN', '24.ED', '24.EG', '24.EH', '24.EJ', '24.EU', '24.EV', '24.EX', '24.EZ', '24.IC', '24.KA', '24.KC'], 'core': '384.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9019, -1, 8184, -1], 'generators': [25903229683158464676480, 6920176418617, 122003583856732942, 1313941668480, 1313941673647, 51090957482037557056, 53952413034673736392198, 54003247877598743421360, 4097467157062], 'label': '6144.ze.12.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.w1', 'projective_image': '2500.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.W', 'subgroup_fusion': None, 'weyl_group': '256.51978'}