Abstract group data - 18432.q

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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': '4.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [6, 8, 4], 'aut_gens': [[5606321841949, 11219135523247], [5612588778839, 12526722447129], [5612549230056, 12694932201600], [8395980364662, 15135927619700]], 'aut_group': '36864.i', 'aut_hash': 7993138791391900980, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 36864, 'aut_permdeg': 192, 'aut_perms': [326707282194999932138931876962189584058466051393347301222119339607497459455484350212976517545609380101924329388431533662314275483816958079512502970997347511467098407605761948950059959381360864912557708668120549214097222629818854374059771253345210280570971375631530170324906299046694544702478497159129853718627821459160281545913841526493254059284085380702779, 111122443266125845180164711713136007839016483988117349099824938767090809234844478596402642053625460455215847482439369522752846065104671272219818902220305388901215037285593414616408735148487737358565462628339152567146235412279178411046342262621231630775252211056261481228967084790229335062529798787272849144412166212172457028694338789587900032692711101426739, 207470899030200466900256398613899079963630180963393058390480225741936487134172703066881639770834567739993105368325030894219660614528967728236200980044647941372740150955411828487382079085003547422321882268806645024400377667657867955985809824468432492179224714681145048540810131388282863809262779757336149144500310040897470937883815920408244596873406306009948], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 12, 1, 2], [2, 18, 1, 2], [2, 36, 1, 3], [2, 72, 1, 1], [2, 96, 1, 2], [2, 144, 1, 1], [3, 64, 1, 1], [3, 1024, 1, 1], [4, 96, 1, 1], [4, 144, 1, 1], [4, 192, 1, 1], [4, 288, 1, 6], [4, 288, 2, 1], [4, 576, 1, 4], [4, 1152, 1, 1], [6, 192, 1, 1], [6, 192, 2, 1], [6, 384, 1, 1], [6, 768, 1, 1], [6, 3072, 1, 1], [8, 1152, 1, 1], [8, 1152, 2, 1], [12, 768, 1, 1], [12, 768, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^5.S_4\\wr C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '36864.i', 'autcentquo_hash': 7993138791391900980, 'autcentquo_nilpotent': False, 'autcentquo_order': 36864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^5.S_4\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 6, 1], [2, 9, 1], [2, 12, 2], [2, 18, 2], [2, 36, 3], [2, 72, 1], [2, 96, 2], [2, 144, 1], [3, 64, 1], [3, 1024, 1], [4, 96, 1], [4, 144, 1], [4, 192, 1], [4, 288, 8], [4, 576, 4], [4, 1152, 1], [6, 192, 3], [6, 384, 1], [6, 768, 1], [6, 3072, 1], [8, 1152, 3], [12, 768, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '18432.q', 'commutator_count': 1, 'commutator_label': '4608.ft', 'complements_known': False, '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', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 17, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 12, 1, 2], [2, 18, 1, 2], [2, 36, 1, 3], [2, 72, 1, 1], [2, 96, 1, 2], [2, 144, 1, 1], [3, 64, 1, 1], [3, 1024, 1, 1], [4, 96, 1, 1], [4, 144, 1, 1], [4, 192, 1, 1], [4, 288, 1, 8], [4, 576, 1, 4], [4, 1152, 1, 1], [6, 192, 1, 1], [6, 192, 2, 1], [6, 384, 1, 1], [6, 768, 1, 1], [6, 3072, 1, 1], [8, 1152, 1, 1], [8, 1152, 2, 1], [12, 768, 1, 1], [12, 768, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 24, 'exponents_of_order': [11, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 4], [12, 1, 4], [18, 0, 2], [18, 1, 6], [24, 1, 1], [36, 1, 6], [72, 1, 1]], 'familial': False, 'frattini_label': '16.14', 'frattini_quotient': '1152.157849', 'hash': 5533240227480333669, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [4, 8], 'inner_gens': [[5606321841949, 11306230357090], [9622710351943, 11219135523247]], 'inner_hash': 5533240227480333669, 'inner_nilpotent': False, 'inner_order': 18432, 'inner_split': True, 'inner_tex': 'C_2^8.\\SOPlus(4,2)', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 1], [4, 4], [6, 4], [9, 4], [12, 10], [18, 9], [24, 1], [36, 6], [72, 1]], 'label': '18432.q', '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': 'C2^8.SO+(4,2)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 40, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 44, 'number_divisions': 41, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': None, 'number_subgroup_classes': 11048, 'number_subgroups': 831378, 'old_label': None, 'order': 18432, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 591], [3, 1088], [4, 6192], [6, 4800], [8, 3456], [12, 2304]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[8395940078618, 12520622435903]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 4], [6, 4], [9, 4], [12, 6], [18, 7], [24, 3], [36, 7], [72, 1]], 'representations': {'PC': {'code': '602088735991813158627636968987361790155018641583491868005786179359738239120765532926018156056063543100599000660757824786324762975228914039136224971983965262973393556010401897869196103791390776836414972789455178654812156067485683888058522831344905931121280', 'gens': [1, 2, 4, 5, 7, 8, 9, 10, 11, 12, 13], 'pres': [13, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 83304, 167597, 66, 612926, 2134, 30787, 406864, 92901, 614644, 594897, 271080, 147658, 186, 26213, 3138, 307975, 1467654, 3295, 60664, 30101, 1647367, 366932, 426849, 69947, 35640, 2122856, 16869, 206422, 111665, 393129, 973462, 362735, 167358, 93661, 3974, 123562, 169907, 90126, 284476, 109028, 7368, 2661995, 1100760, 115165, 301910, 30951, 36580, 2762148, 870037, 711866, 355965, 44680, 47228]}, 'Perm': {'d': 16, 'gens': [5606321841949, 11219135523247]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 256, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^8.\\SOPlus(4,2)', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 109085104
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 17, 'group_order': 18432, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 109085115
    {'aut_label': '2A', 'centralizer': '6.B', 'counter': 2, 'group_counter': 17, 'group_order': 18432, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1313941668480, 'size': 6}
  • id: 109085126
    {'aut_label': '2B', 'centralizer': '9.a1', 'counter': 3, 'group_counter': 17, 'group_order': 18432, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 2789792414767, 'size': 9}
  • id: 109085137
    {'aut_label': '2C', 'centralizer': '12.G', 'counter': 4, 'group_counter': 17, 'group_order': 18432, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 16687, 'size': 12}
  • id: 109085143
    {'aut_label': '2D', 'centralizer': '12.I', 'counter': 5, 'group_counter': 17, 'group_order': 18432, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 87091200, 'size': 12}
  • id: 109085144
    {'aut_label': '2E', 'centralizer': '18.G', 'counter': 6, 'group_counter': 17, 'group_order': 18432, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 2789705329920, 'size': 18}
  • id: 109085145
    {'aut_label': '2F', 'centralizer': '18.E', 'counter': 7, 'group_counter': 17, 'group_order': 18432, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 1313901388807, 'size': 18}
  • id: 109085146
    {'aut_label': '2G', 'centralizer': '36.BC', 'counter': 8, 'group_counter': 17, 'group_order': 18432, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 2789792426280, 'size': 36}
  • id: 109085147
    {'aut_label': '2H', 'centralizer': '36.BB', 'counter': 9, 'group_counter': 17, 'group_order': 18432, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 1313941673656, 'size': 36}
  • id: 109085105
    {'aut_label': '2I', 'centralizer': '36.BA', 'counter': 10, 'group_counter': 17, 'group_order': 18432, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 2789832694463, 'size': 36}
  • id: 109085106
    {'aut_label': '2J', 'centralizer': '72.A', 'counter': 11, 'group_counter': 17, 'group_order': 18432, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 40284856, 'size': 72}
  • id: 109085107
    {'aut_label': '2K', 'centralizer': '96.CI', 'counter': 12, 'group_counter': 17, 'group_order': 18432, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 20748389759147, 'size': 96}
  • id: 109085108
    {'aut_label': '2L', 'centralizer': '96.BB', 'counter': 13, 'group_counter': 17, 'group_order': 18432, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 5786825978863, 'size': 96}
  • id: 109085109
    {'aut_label': '2M', 'centralizer': '144.BH', 'counter': 14, 'group_counter': 17, 'group_order': 18432, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 87181930814, 'size': 144}
  • id: 109085110
    {'aut_label': '3A', 'centralizer': '64.B', 'counter': 15, 'group_counter': 17, 'group_order': 18432, 'label': '3A', 'order': 3, 'powers': [15, 1], 'representative': 10091, 'size': 64}
  • id: 109085111
    {'aut_label': '3B', 'centralizer': None, 'counter': 16, 'group_counter': 17, 'group_order': 18432, 'label': '3B', 'order': 3, 'powers': [16, 1], 'representative': 2708874167044, 'size': 1024}
  • id: 109085112
    {'aut_label': '4A', 'centralizer': '96.BA', 'counter': 17, 'group_counter': 17, 'group_order': 18432, 'label': '4A', 'order': 4, 'powers': [2, 17], 'representative': 8402254543296, 'size': 96}
  • id: 109085113
    {'aut_label': '4B', 'centralizer': '144.BI', 'counter': 18, 'group_counter': 17, 'group_order': 18432, 'label': '4B', 'order': 4, 'powers': [3, 18], 'representative': 3923142866057, 'size': 144}
  • id: 109085114
    {'aut_label': '4C', 'centralizer': '192.BQ', 'counter': 19, 'group_counter': 17, 'group_order': 18432, 'label': '4C', 'order': 4, 'powers': [4, 19], 'representative': 6920176433630, 'size': 192}
  • id: 109085116
    {'aut_label': '4D', 'centralizer': None, 'counter': 20, 'group_counter': 17, 'group_order': 18432, 'label': '4D', 'order': 4, 'powers': [6, 20], 'representative': 1401087306365, 'size': 288}
  • id: 109085117
    {'aut_label': '4E', 'centralizer': None, 'counter': 21, 'group_counter': 17, 'group_order': 18432, 'label': '4E', 'order': 4, 'powers': [7, 21], 'representative': 20916475401478, 'size': 288}
  • id: 109085118
    {'aut_label': '4E', 'centralizer': None, 'counter': 22, 'group_counter': 17, 'group_order': 18432, 'label': '4F', 'order': 4, 'powers': [7, 22], 'representative': 19615075598158, 'size': 288}
  • id: 109085119
    {'aut_label': '4G', 'centralizer': None, 'counter': 23, 'group_counter': 17, 'group_order': 18432, 'label': '4G', 'order': 4, 'powers': [7, 23], 'representative': 1307801392566, 'size': 288}
  • id: 109085120
    {'aut_label': '4H', 'centralizer': None, 'counter': 24, 'group_counter': 17, 'group_order': 18432, 'label': '4H', 'order': 4, 'powers': [3, 24], 'representative': 9709841468873, 'size': 288}
  • id: 109085121
    {'aut_label': '4I', 'centralizer': None, 'counter': 25, 'group_counter': 17, 'group_order': 18432, 'label': '4I', 'order': 4, 'powers': [3, 25], 'representative': 19527817108907, 'size': 288}
  • id: 109085122
    {'aut_label': '4J', 'centralizer': None, 'counter': 26, 'group_counter': 17, 'group_order': 18432, 'label': '4J', 'order': 4, 'powers': [2, 26], 'representative': 1482111147001, 'size': 288}
  • id: 109085123
    {'aut_label': '4K', 'centralizer': None, 'counter': 27, 'group_counter': 17, 'group_order': 18432, 'label': '4K', 'order': 4, 'powers': [2, 27], 'representative': 5612462150392, 'size': 288}
  • id: 109085124
    {'aut_label': '4L', 'centralizer': None, 'counter': 28, 'group_counter': 17, 'group_order': 18432, 'label': '4L', 'order': 4, 'powers': [8, 28], 'representative': 3923142860882, 'size': 576}
  • id: 109085125
    {'aut_label': '4M', 'centralizer': None, 'counter': 29, 'group_counter': 17, 'group_order': 18432, 'label': '4M', 'order': 4, 'powers': [9, 29], 'representative': 6920136145317, 'size': 576}
  • id: 109085127
    {'aut_label': '4N', 'centralizer': None, 'counter': 30, 'group_counter': 17, 'group_order': 18432, 'label': '4N', 'order': 4, 'powers': [5, 30], 'representative': 4016432044942, 'size': 576}
  • id: 109085128
    {'aut_label': '4O', 'centralizer': None, 'counter': 31, 'group_counter': 17, 'group_order': 18432, 'label': '4O', 'order': 4, 'powers': [10, 31], 'representative': 16912584490191, 'size': 576}
  • id: 109085129
    {'aut_label': '4P', 'centralizer': None, 'counter': 32, 'group_counter': 17, 'group_order': 18432, 'label': '4P', 'order': 4, 'powers': [14, 32], 'representative': 15310327744211, 'size': 1152}
  • id: 109085130
    {'aut_label': '6A', 'centralizer': '192.X', 'counter': 33, 'group_counter': 17, 'group_order': 18432, 'label': '6A', 'order': 6, 'powers': [15, 2], 'representative': 1313941674248, 'size': 192}
  • id: 109085131
    {'aut_label': '6B1', 'centralizer': '192.X', 'counter': 34, 'group_counter': 17, 'group_order': 18432, 'label': '6B1', 'order': 6, 'powers': [15, 4], 'representative': 4010205403567, 'size': 192}
  • id: 109085132
    {'aut_label': '6B1', 'centralizer': '192.X', 'counter': 35, 'group_counter': 17, 'group_order': 18432, 'label': '6B-1', 'order': 6, 'powers': [15, 4], 'representative': 2708761322287, 'size': 192}
  • id: 109085133
    {'aut_label': '6C', 'centralizer': None, 'counter': 36, 'group_counter': 17, 'group_order': 18432, 'label': '6C', 'order': 6, 'powers': [15, 5], 'representative': 87092052, 'size': 384}
  • id: 109085134
    {'aut_label': '6D', 'centralizer': None, 'counter': 37, 'group_counter': 17, 'group_order': 18432, 'label': '6D', 'order': 6, 'powers': [15, 13], 'representative': 5786825975151, 'size': 768}
  • id: 109085135
    {'aut_label': '6E', 'centralizer': None, 'counter': 38, 'group_counter': 17, 'group_order': 18432, 'label': '6E', 'order': 6, 'powers': [16, 12], 'representative': 18132997463144, 'size': 3072}
  • id: 109085136
    {'aut_label': '8A', 'centralizer': None, 'counter': 39, 'group_counter': 17, 'group_order': 18432, 'label': '8A', 'order': 8, 'powers': [18, 39], 'representative': 11387184899181, 'size': 1152}
  • id: 109085138
    {'aut_label': '8B1', 'centralizer': None, 'counter': 40, 'group_counter': 17, 'group_order': 18432, 'label': '8B1', 'order': 8, 'powers': [20, 41], 'representative': 15135851779200, 'size': 1152}
  • id: 109085139
    {'aut_label': '8B1', 'centralizer': None, 'counter': 41, 'group_counter': 17, 'group_order': 18432, 'label': '8B-1', 'order': 8, 'powers': [20, 40], 'representative': 14002526367485, 'size': 1152}
  • id: 109085140
    {'aut_label': '12A', 'centralizer': None, 'counter': 42, 'group_counter': 17, 'group_order': 18432, 'label': '12A', 'order': 12, 'powers': [33, 17], 'representative': 9703741454508, 'size': 768}
  • id: 109085141
    {'aut_label': '12B1', 'centralizer': None, 'counter': 43, 'group_counter': 17, 'group_order': 18432, 'label': '12B1', 'order': 12, 'powers': [34, 19], 'representative': 9535528431225, 'size': 768}
  • id: 109085142
    {'aut_label': '12B1', 'centralizer': None, 'counter': 44, 'group_counter': 17, 'group_order': 18432, 'label': '12B-1', 'order': 12, 'powers': [35, 19], 'representative': 8221631038430, 'size': 768}
• 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: 4134464
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4134475
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 4134486
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 4134497
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4134500
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, 2, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134501
    {'cdim': 4, 'counter': 6, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.4a', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 2, 0, 1, -2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 1, 1, -1, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
  • id: 4134502
    {'cdim': 4, 'counter': 7, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.4b', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 0, 0, -2, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, -2, -2, -2, -2, 0, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134503
    {'cdim': 4, 'counter': 8, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.4c', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, 0, 0, -2, 1, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, -2, -2, -2, 0, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134504
    {'cdim': 4, 'counter': 9, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.4d', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, -2, 0, 1, -2, -2, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
  • id: 4134465
    {'cdim': 6, 'counter': 10, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.6a', 'multiplicity': 1, 'nt': [8, 47], 'qdim': 6, 'qvalues': [6, 6, 6, 2, 2, -2, -2, 2, -2, 2, -2, 0, 4, 2, 3, 0, 4, 2, 2, 0, 0, -2, 0, 0, 0, -2, 2, 0, -2, 0, 0, 0, -1, -1, 3, -1, 1, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
  • id: 4134466
    {'cdim': 6, 'counter': 11, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.6b', 'multiplicity': 1, 'nt': [12, 200], 'qdim': 6, 'qvalues': [6, 6, 6, 2, 2, -2, -2, 2, -2, 2, -2, 0, 2, -2, 3, 0, 2, -2, 4, -2, 0, 2, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, -1, -1, 3, -1, -1, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
  • id: 4134467
    {'cdim': 6, 'counter': 12, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.6c', 'multiplicity': 1, 'nt': [12, 201], 'qdim': 6, 'qvalues': [6, 6, 6, 2, 2, -2, -2, 2, -2, 2, -2, 0, -2, -2, 3, 0, -2, -2, -4, 2, 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, -1, -1, 3, -1, 1, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
  • id: 4134468
    {'cdim': 6, 'counter': 13, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.6d', 'multiplicity': 1, 'nt': [12, 202], 'qdim': 6, 'qvalues': [6, 6, 6, 2, 2, -2, -2, 2, -2, 2, -2, 0, -4, 2, 3, 0, -4, 2, -2, 0, 0, -2, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, -1, -1, 3, -1, -1, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
  • id: 4134469
    {'cdim': 9, 'counter': 14, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.9a', 'multiplicity': 1, 'nt': [16, 1294], 'qdim': 9, 'qvalues': [9, 9, 9, -3, -3, 1, 1, -3, 1, -3, 1, 3, 3, 1, 0, 0, 3, 1, -3, -1, -1, 1, 3, -1, -1, 1, 1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 4134470
    {'cdim': 9, 'counter': 15, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.9b', 'multiplicity': 1, 'nt': [18, 272], 'qdim': 9, 'qvalues': [9, 9, 9, -3, -3, 1, 1, -3, 1, -3, 1, 3, -3, 1, 0, 0, -3, 1, 3, 1, -1, 1, 3, 1, -1, 1, 1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 4134471
    {'cdim': 9, 'counter': 16, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.9c', 'multiplicity': 1, 'nt': [18, 273], 'qdim': 9, 'qvalues': [9, 9, 9, -3, -3, 1, 1, -3, 1, -3, 1, -3, -3, 1, 0, 0, -3, 1, 3, 1, 1, 1, -3, 1, 1, 1, 1, -1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 4134472
    {'cdim': 9, 'counter': 17, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.9d', 'multiplicity': 1, 'nt': [18, 274], 'qdim': 9, 'qvalues': [9, 9, 9, -3, -3, 1, 1, -3, 1, -3, 1, -3, 3, 1, 0, 0, 3, 1, -3, -1, 1, 1, -3, -1, 1, 1, 1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 4134473
    {'cdim': 12, 'counter': 18, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.12a', 'multiplicity': 1, 'nt': [16, 1792], 'qdim': 12, 'qvalues': [12, 4, -4, 4, 8, 4, 4, -4, -4, 0, 0, 0, 0, 4, 6, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134474
    {'cdim': 12, 'counter': 19, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.12b', 'multiplicity': 1, 'nt': [16, 1796], 'qdim': 12, 'qvalues': [12, 4, -4, 8, 4, -4, -4, 0, 4, -4, 0, 0, 2, 0, 6, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 4134476
    {'cdim': 12, 'counter': 20, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.12c', 'multiplicity': 1, 'nt': [24, 2821], 'qdim': 12, 'qvalues': [12, 12, 12, 4, 4, -4, -4, 4, -4, 4, -4, 0, 2, 0, -3, 0, 2, 0, -2, 2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 1, 1, -3, 1, -1, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
  • id: 4134477
    {'cdim': 12, 'counter': 21, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.12d', 'multiplicity': 1, 'nt': [24, 12243], 'qdim': 12, 'qvalues': [12, 4, -4, 4, 8, 4, 4, -4, -4, 0, 0, 0, 0, -4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134478
    {'cdim': 12, 'counter': 22, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.12e', 'multiplicity': 1, 'nt': [24, 12247], 'qdim': 12, 'qvalues': [12, 4, -4, 8, 4, -4, -4, 0, 4, -4, 0, 0, -2, 0, 6, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
  • id: 4134479
    {'cdim': 12, 'counter': 23, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.12f', 'multiplicity': 1, 'nt': [36, 1763], 'qdim': 12, 'qvalues': [12, 12, 12, 4, 4, -4, -4, 4, -4, 4, -4, 0, -2, 0, -3, 0, -2, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, -3, 1, 1, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
  • id: 4134482
    {'cdim': 18, 'counter': 26, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.18a', 'multiplicity': 1, 'nt': [24, 12470], 'qdim': 18, 'qvalues': [18, -6, 2, -6, 6, -6, 10, 2, 2, -2, -2, 6, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, -2, 0, 2, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134483
    {'cdim': 18, 'counter': 27, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.18b', 'multiplicity': 1, 'nt': [32, 1119761], 'qdim': 18, 'qvalues': [18, -6, 2, -6, 6, 10, -6, 2, 2, -2, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134484
    {'cdim': 18, 'counter': 28, 'faithful': False, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.18c', 'multiplicity': 1, 'nt': [36, 1758], 'qdim': 18, 'qvalues': [18, 18, 18, -6, -6, 2, 2, -6, 2, -6, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134485
    {'cdim': 18, 'counter': 29, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.18d', 'multiplicity': 1, 'nt': [36, 11197], 'qdim': 18, 'qvalues': [18, -6, 2, -6, 6, -6, 10, 2, 2, -2, -2, -6, 0, 2, 0, 0, 0, 2, 0, 0, -2, 2, 2, 0, -2, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134487
    {'cdim': 18, 'counter': 30, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.18e', 'multiplicity': 1, 'nt': [36, 11198], 'qdim': 18, 'qvalues': [18, -6, 2, -6, 6, -6, 10, 2, 2, -2, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, -4, -2, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134488
    {'cdim': 18, 'counter': 31, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.18f', 'multiplicity': 1, 'nt': [36, 11198], 'qdim': 18, 'qvalues': [18, -6, 2, -6, 6, -6, 10, 2, 2, -2, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 4, -2, 0, 0, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134489
    {'cdim': 18, 'counter': 32, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.18g', 'multiplicity': 1, 'nt': [36, 11204], 'qdim': 18, 'qvalues': [18, -6, 2, -6, 6, 10, -6, 2, 2, -2, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134480
    {'cdim': 12, 'counter': 24, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.12g', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, 8, -8, 16, 8, -8, -8, 0, 8, -8, 0, 0, 4, 0, -6, 0, -4, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
  • id: 4134481
    {'cdim': 12, 'counter': 25, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.12h', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 8, -8, 16, 8, -8, -8, 0, 8, -8, 0, 0, -4, 0, -6, 0, 4, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 4134491
    {'cdim': 24, 'counter': 34, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.24a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, 8, -8, 8, 16, 8, 8, -8, -8, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134490
    {'cdim': 18, 'counter': 33, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.18h', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, -12, 4, -12, 12, 20, -12, 4, 4, -4, -4, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134492
    {'cdim': 36, 'counter': 35, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.36a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 36, 'qvalues': [36, -12, 4, 12, -12, 4, 4, -4, 4, 4, -4, 6, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134493
    {'cdim': 36, 'counter': 36, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.36b', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 36, 'qvalues': [36, 12, -12, -12, 0, -4, -4, -4, 4, 8, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134494
    {'cdim': 36, 'counter': 37, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.36c', 'multiplicity': 1, 'nt': [64, 0], 'qdim': 36, 'qvalues': [36, 12, -12, 0, -12, 4, 4, 8, -4, -4, 0, 0, 6, 0, 0, 0, -6, 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], 'schur_index': 1}
  • id: 4134495
    {'cdim': 36, 'counter': 38, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.36d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, -12, 4, 12, -12, 4, 4, -4, 4, 4, -4, -6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134496
    {'cdim': 36, 'counter': 39, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.36e', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, 12, -12, -12, 0, -4, -4, -4, 4, 8, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4134498
    {'cdim': 36, 'counter': 40, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.36f', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 36, 'qvalues': [36, 12, -12, 0, -12, 4, 4, 8, -4, -4, 0, 0, -6, 0, 0, 0, 6, 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], 'schur_index': 1}
  • id: 4134499
    {'cdim': 72, 'counter': 41, 'faithful': True, 'group': '18432.q', 'group_order': 18432, 'image': None, 'label': '18432.q.72a', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 72, 'qvalues': [72, -24, 8, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5992801
    {'center': None, 'center_index': 1, 'center_order': 18432, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 18432, 'label': '18432.q.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5992812
    {'center': None, 'center_index': 1, 'center_order': 18432, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 9216, 'label': '18432.q.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5992823
    {'center': None, 'center_index': 1, 'center_order': 18432, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 9216, 'label': '18432.q.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5992834
    {'center': None, 'center_index': 1, 'center_order': 18432, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 9216, 'label': '18432.q.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5992840
    {'center': None, 'center_index': 4, 'center_order': 4608, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': None, 'kernel_order': 2304, 'label': '18432.q.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 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]]]}
  • id: 5992841
    {'center': None, 'center_index': 72, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': None, 'kernel_order': 256, 'label': '18432.q.4a', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5992842
    {'center': None, 'center_index': 72, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': None, 'kernel_order': 256, 'label': '18432.q.4b', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992843
    {'center': None, 'center_index': 72, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': None, 'kernel_order': 256, 'label': '18432.q.4c', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992844
    {'center': None, 'center_index': 72, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': None, 'kernel_order': 256, 'label': '18432.q.4d', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5992802
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 10, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.6a', 'nt': [8, 47], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5992803
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 11, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.6b', 'nt': [12, 200], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5992804
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 12, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.6c', 'nt': [12, 201], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5992805
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 13, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.6d', 'nt': [12, 202], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5992806
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 14, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.9a', 'nt': [16, 1294], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992807
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 15, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.9b', 'nt': [18, 272], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992808
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 16, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.9c', 'nt': [18, 273], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992809
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 17, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.9d', 'nt': [18, 274], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992810
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.12a', 'nt': [16, 1792], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[8, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[6, 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]], [[2, 0]], [[0, 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]]]}
  • id: 5992811
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.12b', 'nt': [16, 1796], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[8, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992813
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 20, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.12c', 'nt': [24, 2821], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5992814
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.12d', 'nt': [24, 12243], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[8, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[6, 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]], [[-2, 0]], [[0, 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]]]}
  • id: 5992815
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.12e', 'nt': [24, 12247], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[8, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992816
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 23, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.12f', 'nt': [36, 1763], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[12, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5992817
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.12g1', 'nt': [48, 0], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[8, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[-3, 0], [-4, 1]], [[1, 0], [4, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]]]}
  • id: 5992818
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.12g2', 'nt': [48, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[8, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[1, 0], [4, 1]], [[-3, 0], [-4, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]]]}
  • id: 5992819
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.12h1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[8, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-3, 0], [-4, 1]], [[1, 0], [4, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]]]}
  • id: 5992820
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.12h2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-4, 0]], [[8, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[1, 0], [4, 1]], [[-3, 0], [-4, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]]]}
  • id: 5992821
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 1, 'dim': 18, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.18a', 'nt': [24, 12470], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]]]}
  • id: 5992822
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 1, 'dim': 18, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.18b', 'nt': [32, 1119761], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[6, 0]], [[10, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992824
    {'center': None, 'center_index': 1152, 'center_order': 16, 'counter': 30, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '1152.157849', 'image_order': 1152, 'indicator': 1, 'kernel': None, 'kernel_order': 16, 'label': '18432.q.18c', 'nt': [36, 1758], 'q_character': None, 'values': [[[18, 0]], [[18, 0]], [[18, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 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]]]}
  • id: 5992825
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 1, 'dim': 18, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.18d', 'nt': [36, 11197], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]]]}
  • id: 5992826
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 1, 'dim': 18, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.18e', 'nt': [36, 11198], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 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]]]}
  • id: 5992827
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 1, 'dim': 18, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.18f', 'nt': [36, 11198], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 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]]]}
  • id: 5992828
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 1, 'dim': 18, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.18g', 'nt': [36, 11204], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[6, 0]], [[10, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992829
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 4, 'dim': 18, 'faithful': True, 'field': [1, 0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.18h1', 'nt': [72, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[6, 0]], [[10, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 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]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992830
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 4, 'dim': 18, 'faithful': True, 'field': [1, 0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.18h2', 'nt': [72, 2], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[6, 0]], [[10, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 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]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992831
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.24a', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[16, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992832
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.36a', 'nt': [48, 0], 'q_character': None, 'values': [[[36, 0]], [[-12, 0]], [[4, 0]], [[12, 0]], [[-12, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[6, 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]], [[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]], [[0, 0]]]}
  • id: 5992833
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.36b', 'nt': [48, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 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]], [[-2, 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]]]}
  • id: 5992835
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.36c', 'nt': [64, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[-12, 0]], [[4, 0]], [[4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992836
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 41, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.36d', 'nt': [72, 0], 'q_character': None, 'values': [[[36, 0]], [[-12, 0]], [[4, 0]], [[12, 0]], [[-12, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-6, 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]], [[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]], [[0, 0]]]}
  • id: 5992837
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.36e', 'nt': [72, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[2, 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]]]}
  • id: 5992838
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.36f', 'nt': [72, 0], 'q_character': None, 'values': [[[36, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[-12, 0]], [[4, 0]], [[4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5992839
    {'center': None, 'center_index': 18432, 'center_order': 1, 'counter': 44, 'cyclotomic_n': 1, 'dim': 72, 'faithful': True, 'field': [0, 1], 'group': '18432.q', 'group_counter': 17, 'group_order': 18432, 'image': None, 'image_isoclass': '18432.q', 'image_order': 18432, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '18432.q.72a', 'nt': [96, 0], 'q_character': None, 'values': [[[72, 0]], [[-24, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 63387164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 18432, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '18432.q.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': None, 'standard_generators': False, 'stem': False, 'subgroup': '18432.q', 'subgroup_hash': 5533240227480333669, 'subgroup_order': 18432, 'subgroup_tex': 'C_2^8.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 63387275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 9216, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.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': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9216.w', 'subgroup_hash': 3811396787289762613, 'subgroup_order': 9216, 'subgroup_tex': 'C_2^8.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 9216, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.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': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9216.es', 'subgroup_hash': 7696602514649327903, 'subgroup_order': 9216, 'subgroup_tex': 'C_2^4.S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 9216, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.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': None, 'standard_generators': False, 'stem': False, 'subgroup': '9216.v', 'subgroup_hash': 8751132342904155621, 'subgroup_order': 9216, 'subgroup_tex': 'C_2^4.A_4^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 4608, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.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': ['D', 'L1', 'D1', 'C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4608.ft', 'subgroup_hash': 3089245560217249605, 'subgroup_order': 4608, 'subgroup_tex': 'C_2^4:\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63387719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2304, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '4608.ei', 'subgroup_hash': 5425608297552968375, 'subgroup_order': 4608, 'subgroup_tex': 'C_2^8:(C_3\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 63387830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2304, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.4.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '4608.fq', 'subgroup_hash': 1626788905697944905, 'subgroup_order': 4608, 'subgroup_tex': 'C_2^6:(C_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 256, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '3072.ec', 'subgroup_hash': 8803011544601651028, 'subgroup_order': 3072, 'subgroup_tex': 'C_2^8:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '3072.ev', 'subgroup_hash': 2078568082780026723, 'subgroup_order': 3072, 'subgroup_tex': 'C_2^5:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2304, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', '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': ['L2', 'D2', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2304.lb', 'subgroup_hash': 639387765762631470, 'subgroup_order': 2304, 'subgroup_tex': 'C_2^4:A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.8.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2304.hx', 'subgroup_hash': 6408293651439809080, 'subgroup_order': 2304, 'subgroup_tex': 'C_2^2.S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '18432.q.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.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': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7083753762161107245, 'subgroup_order': 2048, 'subgroup_tex': 'C_2^5.C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 63387198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '1536.408546880', 'subgroup_hash': 1184767368680492186, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^4.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '1536.408545323', 'subgroup_hash': 4237846459964537217, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^4.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '1536.408610986', 'subgroup_hash': 4139234108182936439, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^7:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '1536.408545323', 'subgroup_hash': 4237846459964537217, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^4.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 256, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '1536.408531111', 'subgroup_hash': 8142315083209974381, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 256, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '1536.408641062', 'subgroup_hash': 3541994663478164713, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '1536.408531110', 'subgroup_hash': 1088834560890831063, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '1536.408640849', 'subgroup_hash': 4058867741420552589, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^4:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '1536.408640849', 'subgroup_hash': 4058867741420552589, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^4:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 256, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '1536.408641062', 'subgroup_hash': 3541994663478164713, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.16.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157861', 'subgroup_hash': 4207673190380457283, 'subgroup_order': 1152, 'subgroup_tex': '(C_2^2\\times A_4):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.16.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.155467', 'subgroup_hash': 4377764292455698327, 'subgroup_order': 1152, 'subgroup_tex': '(C_2^2\\times S_4):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.16.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, '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': '1152.155467', 'subgroup_hash': 4377764292455698327, 'subgroup_order': 1152, 'subgroup_tex': '(C_2^2\\times S_4):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.16.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '1152.157855', 'subgroup_hash': 3247369171485304284, 'subgroup_order': 1152, 'subgroup_tex': 'A_4\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.16.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1152.157861', 'subgroup_hash': 4207673190380457283, 'subgroup_order': 1152, 'subgroup_tex': '(C_2^2\\times A_4):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.16.F', 'maximal': True, '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': '1152.157849', 'subgroup_hash': 5496387407741636925, 'subgroup_order': 1152, 'subgroup_tex': 'S_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 63387375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1024.ddu', 'subgroup_hash': 5301258843298981512, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1024.deg', 'subgroup_hash': 6885888035353292978, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^7.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.18.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1024.deg', 'subgroup_hash': 6885888035353292978, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^7.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.18.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7986331815209087165, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^5.C_2^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.18.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1024.dff', 'subgroup_hash': 6084013020118845533, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.18.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1024.dff', 'subgroup_hash': 6084013020118845533, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.18.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1024.dgv', 'subgroup_hash': 4293763413942745332, 'subgroup_order': 1024, 'subgroup_tex': 'C_2^2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1087581', 'subgroup_hash': 1087581, 'subgroup_order': 768, 'subgroup_tex': 'C_2\\wr D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1087597', 'subgroup_hash': 1087597, 'subgroup_order': 768, 'subgroup_tex': 'C_2^6.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1087596', 'subgroup_hash': 1087596, 'subgroup_order': 768, 'subgroup_tex': 'C_2^6.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1087582', 'subgroup_hash': 1087582, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090187', 'subgroup_hash': 1090187, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1089950', 'subgroup_hash': 1089950, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1084399', 'subgroup_hash': 1084399, 'subgroup_order': 768, 'subgroup_tex': 'C_2^7:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1083649', 'subgroup_hash': 1083649, 'subgroup_order': 768, 'subgroup_tex': 'C_2^6:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1087597', 'subgroup_hash': 1087597, 'subgroup_order': 768, 'subgroup_tex': 'C_2^6.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1087583', 'subgroup_hash': 1087583, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1087581', 'subgroup_hash': 1087581, 'subgroup_order': 768, 'subgroup_tex': 'C_2\\wr D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1084399', 'subgroup_hash': 1084399, 'subgroup_order': 768, 'subgroup_tex': 'C_2^7:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1090187', 'subgroup_hash': 1090187, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1090187', 'subgroup_hash': 1090187, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1083649', 'subgroup_hash': 1083649, 'subgroup_order': 768, 'subgroup_tex': 'C_2^6:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1089950', 'subgroup_hash': 1089950, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1089950', 'subgroup_hash': 1089950, 'subgroup_order': 768, 'subgroup_tex': 'C_2^3.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1085323', 'subgroup_hash': 1085323, 'subgroup_order': 768, 'subgroup_tex': 'C_2^8.C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 256, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1085321', 'subgroup_hash': 1085321, 'subgroup_order': 768, 'subgroup_tex': 'C_2^6:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1090070', 'subgroup_hash': 1090070, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.24.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '768.1090070', 'subgroup_hash': 1090070, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.32.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '576.5126', 'subgroup_hash': 5126, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.32.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '576.8663', 'subgroup_hash': 8663, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387708
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.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': '576.8663', 'subgroup_hash': 8663, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387720
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.32.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '576.8663', 'subgroup_hash': 8663, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.32.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63387742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.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': '576.8653', 'subgroup_hash': 8653, 'subgroup_order': 576, 'subgroup_tex': 'S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.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': '576.8652', 'subgroup_hash': 8652, 'subgroup_order': 576, 'subgroup_tex': 'A_4^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.32.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '576.8652', 'subgroup_hash': 8652, 'subgroup_order': 576, 'subgroup_tex': 'A_4^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.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': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63387786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.22886', 'subgroup_hash': 7794799869245242452, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.6407063', 'subgroup_hash': 6400076820063978839, 'subgroup_order': 512, 'subgroup_tex': 'C_2^7:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.22886', 'subgroup_hash': 7794799869245242452, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.41018', 'subgroup_hash': 5206436278243982164, 'subgroup_order': 512, 'subgroup_tex': 'C_2^7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.41229', 'subgroup_hash': 1311698700316408213, 'subgroup_order': 512, 'subgroup_tex': 'C_2^7.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.418986', 'subgroup_hash': 124029878967622033, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.46927', 'subgroup_hash': 3242287688521790253, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.57589', 'subgroup_hash': 3092913061049316236, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.51574', 'subgroup_hash': 8723707814686244922, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.51578', 'subgroup_hash': 667617278801260587, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.418986', 'subgroup_hash': 124029878967622033, 'subgroup_order': 512, 'subgroup_tex': 'D_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.46927', 'subgroup_hash': 3242287688521790253, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.57589', 'subgroup_hash': 3092913061049316236, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.57589', 'subgroup_hash': 3092913061049316236, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.22886', 'subgroup_hash': 7794799869245242452, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.6407063', 'subgroup_hash': 6400076820063978839, 'subgroup_order': 512, 'subgroup_tex': 'C_2^7:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.22886', 'subgroup_hash': 7794799869245242452, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.6407063', 'subgroup_hash': 6400076820063978839, 'subgroup_order': 512, 'subgroup_tex': 'C_2^7:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.22886', 'subgroup_hash': 7794799869245242452, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.22886', 'subgroup_hash': 7794799869245242452, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.41018', 'subgroup_hash': 5206436278243982164, 'subgroup_order': 512, 'subgroup_tex': 'C_2^7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.41229', 'subgroup_hash': 1311698700316408213, 'subgroup_order': 512, 'subgroup_tex': 'C_2^7.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.22886', 'subgroup_hash': 7794799869245242452, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.22886', 'subgroup_hash': 7794799869245242452, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.6407063', 'subgroup_hash': 6400076820063978839, 'subgroup_order': 512, 'subgroup_tex': 'C_2^7:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.22886', 'subgroup_hash': 7794799869245242452, 'subgroup_order': 512, 'subgroup_tex': 'C_2^6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.6249567', 'subgroup_hash': 6452065007057432321, 'subgroup_order': 512, 'subgroup_tex': 'C_2^4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.6249567', 'subgroup_hash': 6452065007057432321, 'subgroup_order': 512, 'subgroup_tex': 'C_2^4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.36.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.6249567', 'subgroup_hash': 6452065007057432321, 'subgroup_order': 512, 'subgroup_tex': 'C_2^4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18122', 'subgroup_hash': 18122, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20100', 'subgroup_hash': 20100, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5790', 'subgroup_hash': 5790, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20100', 'subgroup_hash': 20100, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5790', 'subgroup_hash': 5790, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18122', 'subgroup_hash': 18122, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5657', 'subgroup_hash': 5657, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5656', 'subgroup_hash': 5656, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5567', 'subgroup_hash': 5567, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5566', 'subgroup_hash': 5566, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.17948', 'subgroup_hash': 17948, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5657', 'subgroup_hash': 5657, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5566', 'subgroup_hash': 5566, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5565', 'subgroup_hash': 5565, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5790', 'subgroup_hash': 5790, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20100', 'subgroup_hash': 20100, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20163', 'subgroup_hash': 20163, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20099', 'subgroup_hash': 20099, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20099', 'subgroup_hash': 20099, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18158', 'subgroup_hash': 18158, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20100', 'subgroup_hash': 20100, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20100', 'subgroup_hash': 20100, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5744', 'subgroup_hash': 5744, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5744', 'subgroup_hash': 5744, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20166', 'subgroup_hash': 20166, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20166', 'subgroup_hash': 20166, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5721', 'subgroup_hash': 5721, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5625', 'subgroup_hash': 5625, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20053', 'subgroup_hash': 20053, 'subgroup_order': 384, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5625', 'subgroup_hash': 5625, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5790', 'subgroup_hash': 5790, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18159', 'subgroup_hash': 18159, 'subgroup_order': 384, 'subgroup_tex': 'C_2^6:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18122', 'subgroup_hash': 18122, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20163', 'subgroup_hash': 20163, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18122', 'subgroup_hash': 18122, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2:\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20100', 'subgroup_hash': 20100, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20099', 'subgroup_hash': 20099, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20166', 'subgroup_hash': 20166, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18221', 'subgroup_hash': 18221, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18221', 'subgroup_hash': 18221, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18221', 'subgroup_hash': 18221, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.48.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20164', 'subgroup_hash': 20164, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1024', 'subgroup_hash': 1024, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.411', 'subgroup_hash': 411, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63387221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 63387222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1024', 'subgroup_hash': 1024, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63387224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 63387225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63387226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 63387227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.64.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 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': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63387228
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 256, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\SOPlus(4,2)', 'simple': False, 'solvable': True, 'special_labels': ['F', 'D3', 'C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.56092', 'subgroup_hash': 56092, 'subgroup_order': 256, 'subgroup_tex': 'C_2^8', 'supersolvable': True, 'sylow': 0}
  • id: 63387229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5675', 'subgroup_hash': 5675, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.4487', 'subgroup_hash': 4487, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5675', 'subgroup_hash': 5675, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.4487', 'subgroup_hash': 4487, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5741', 'subgroup_hash': 5741, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.382', 'subgroup_hash': 382, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.414', 'subgroup_hash': 414, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.382', 'subgroup_hash': 382, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5741', 'subgroup_hash': 5741, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.414', 'subgroup_hash': 414, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16883', 'subgroup_hash': 16883, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16885', 'subgroup_hash': 16885, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5695', 'subgroup_hash': 5695, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5693', 'subgroup_hash': 5693, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5695', 'subgroup_hash': 5695, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5693', 'subgroup_hash': 5693, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.298', 'subgroup_hash': 298, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.302', 'subgroup_hash': 302, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14734', 'subgroup_hash': 14734, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14734', 'subgroup_hash': 14734, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55805', 'subgroup_hash': 55805, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14734', 'subgroup_hash': 14734, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14734', 'subgroup_hash': 14734, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5675', 'subgroup_hash': 5675, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1089', 'subgroup_hash': 1089, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1089', 'subgroup_hash': 1089, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.4487', 'subgroup_hash': 4487, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1529', 'subgroup_hash': 1529, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1535', 'subgroup_hash': 1535, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1535', 'subgroup_hash': 1535, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14734', 'subgroup_hash': 14734, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14734', 'subgroup_hash': 14734, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14734', 'subgroup_hash': 14734, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.55805', 'subgroup_hash': 55805, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2:C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14734', 'subgroup_hash': 14734, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.14734', 'subgroup_hash': 14734, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5675', 'subgroup_hash': 5675, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1089', 'subgroup_hash': 1089, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1089', 'subgroup_hash': 1089, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1089', 'subgroup_hash': 1089, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.1089', 'subgroup_hash': 1089, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.4487', 'subgroup_hash': 4487, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.29598', 'subgroup_hash': 29598, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.7667', 'subgroup_hash': 7667, 'subgroup_order': 256, 'subgroup_tex': 'C_2^6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26539', 'subgroup_hash': 26539, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.382', 'subgroup_hash': 382, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5741', 'subgroup_hash': 5741, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.414', 'subgroup_hash': 414, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16972', 'subgroup_hash': 16972, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.72.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.991', 'subgroup_hash': 991, 'subgroup_order': 192, 'subgroup_tex': 'C_2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.991', 'subgroup_hash': 991, 'subgroup_order': 192, 'subgroup_tex': 'C_2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.991', 'subgroup_hash': 991, 'subgroup_order': 192, 'subgroup_tex': 'C_2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.991', 'subgroup_hash': 991, 'subgroup_order': 192, 'subgroup_tex': 'C_2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.591', 'subgroup_hash': 591, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63387362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1495', 'subgroup_hash': 1495, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1539', 'subgroup_hash': 1539, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 63387367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1000', 'subgroup_hash': 1000, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.191', 'subgroup_hash': 191, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387373
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1539', 'subgroup_hash': 1539, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 63387374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.991', 'subgroup_hash': 991, 'subgroup_order': 192, 'subgroup_tex': 'C_2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1471', 'subgroup_hash': 1471, 'subgroup_order': 192, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 63387381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.994', 'subgroup_hash': 994, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1000', 'subgroup_hash': 1000, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.191', 'subgroup_hash': 191, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1495', 'subgroup_hash': 1495, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1495', 'subgroup_hash': 1495, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387392
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387394
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1473', 'subgroup_hash': 1473, 'subgroup_order': 192, 'subgroup_tex': 'D_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63387399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1488', 'subgroup_hash': 1488, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times \\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.994', 'subgroup_hash': 994, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.991', 'subgroup_hash': 991, 'subgroup_order': 192, 'subgroup_tex': 'C_2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.991', 'subgroup_hash': 991, 'subgroup_order': 192, 'subgroup_tex': 'C_2.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1539', 'subgroup_hash': 1539, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 63387405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 63387406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1473', 'subgroup_hash': 1473, 'subgroup_order': 192, 'subgroup_tex': 'D_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387413
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387416
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1541', 'subgroup_hash': 1541, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.96.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.128.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.128.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.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': 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': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.128.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.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': 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': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.128.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.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': 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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387426
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.128.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.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': 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': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387427
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.128.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.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': 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': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.128.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.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': 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': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.128.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.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': 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': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.128.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.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': 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': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63387432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.h2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.929', 'subgroup_hash': 929, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.742', 'subgroup_hash': 742, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2222', 'subgroup_hash': 2222, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.551', 'subgroup_hash': 551, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.515', 'subgroup_hash': 515, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.194', 'subgroup_hash': 194, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.194', 'subgroup_hash': 194, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1758', 'subgroup_hash': 1758, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1751', 'subgroup_hash': 1751, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.645', 'subgroup_hash': 645, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.643', 'subgroup_hash': 643, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.859', 'subgroup_hash': 859, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.853', 'subgroup_hash': 853, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2264', 'subgroup_hash': 2264, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.36', 'subgroup_hash': 36, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.48', 'subgroup_hash': 48, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.932', 'subgroup_hash': 932, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ct2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2264', 'subgroup_hash': 2264, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.36', 'subgroup_hash': 36, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387532
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387533
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2264', 'subgroup_hash': 2264, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.36', 'subgroup_hash': 36, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.48', 'subgroup_hash': 48, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387551
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387552
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2222', 'subgroup_hash': 2222, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2222', 'subgroup_hash': 2222, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.515', 'subgroup_hash': 515, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.551', 'subgroup_hash': 551, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.194', 'subgroup_hash': 194, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63387569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.551', 'subgroup_hash': 551, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1758', 'subgroup_hash': 1758, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1751', 'subgroup_hash': 1751, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.645', 'subgroup_hash': 645, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.643', 'subgroup_hash': 643, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.859', 'subgroup_hash': 859, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.853', 'subgroup_hash': 853, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.859', 'subgroup_hash': 859, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.853', 'subgroup_hash': 853, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2222', 'subgroup_hash': 2222, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.551', 'subgroup_hash': 551, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.FZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.932', 'subgroup_hash': 932, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.GZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2222', 'subgroup_hash': 2222, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.551', 'subgroup_hash': 551, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.HZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.ID', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2222', 'subgroup_hash': 2222, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.II', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.551', 'subgroup_hash': 551, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.IZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2222', 'subgroup_hash': 2222, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.551', 'subgroup_hash': 551, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387709
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.JZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387736
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2264', 'subgroup_hash': 2264, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.36', 'subgroup_hash': 36, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2222', 'subgroup_hash': 2222, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.KZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.551', 'subgroup_hash': 551, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387765
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 16, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387770
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 16, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2328', 'subgroup_hash': 2328, 'subgroup_order': 128, 'subgroup_tex': 'C_2^7', 'supersolvable': True, 'sylow': 0}
  • id: 63387771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2264', 'subgroup_hash': 2264, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.LZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.36', 'subgroup_hash': 36, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.48', 'subgroup_hash': 48, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.ME', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.929', 'subgroup_hash': 929, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.ML', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.48', 'subgroup_hash': 48, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.48', 'subgroup_hash': 48, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.MZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.ND', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.48', 'subgroup_hash': 48, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.753', 'subgroup_hash': 753, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63387817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.nf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.932', 'subgroup_hash': 932, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.929', 'subgroup_hash': 929, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.NZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2264', 'subgroup_hash': 2264, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.36', 'subgroup_hash': 36, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63387844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2222', 'subgroup_hash': 2222, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63387845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.513', 'subgroup_hash': 513, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2216', 'subgroup_hash': 2216, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.ON', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.630', 'subgroup_hash': 630, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.551', 'subgroup_hash': 551, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63387857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.144.OT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63387858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387859
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387860
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387862
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387863
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.41', 'subgroup_hash': 41, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63387874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 63387876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.211', 'subgroup_hash': 211, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63387877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.13', 'subgroup_hash': 13, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 63387878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387882
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 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': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 63387884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63387887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63387889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387892
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 63387905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 63387922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 16, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387937
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 63387954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.192.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 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': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.256.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.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': 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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.256.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.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': 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': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.256.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.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': 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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.256.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.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': 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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.256.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.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': 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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63387969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.256.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '256.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': 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': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 63387970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 16, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '18432.q.1152.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1152.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1152.157849', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5496387407741636925, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1152, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'S', 'C5'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 63387971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '18432.q.2048.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 63387972
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '18432.q', 'ambient_counter': 17, 'ambient_order': 18432, 'ambient_tex': 'C_2^8.\\SOPlus(4,2)', 'central': True, 'central_factor': False, 'centralizer_order': 18432, 'characteristic': True, 'core_order': 1, 'counter': 827, 'cyclic': True, 'direct': None, 'hall': 1, 'label': '18432.q.18432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18432.a1.N', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '18432.q', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5533240227480333669, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 18432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^8.\\SOPlus(4,2)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D4', 'C6'], 'split': None, '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: 63387164
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.A', '2.B', '2.C', '9.a1', '16.F'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4758, 5186, 4568, 5382], 'generators': [11536, 16, 5606321841949, 843, 127387560, 11219135523247, 4103734078080, 5167, 7, 1313941668480, 87102720, 93409310300, 6227384421], 'label': '18432.q.1.a1', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.A', '2.B', '2.C'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '18432.q', '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': '40000.br'}
  • id: 63387165
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '4.B', '4.C'], 'contains': ['24.R', '24.S', '32.B', '32.C', '32.D'], 'core': '8.A', 'coset_action_label': None, 'count': 1, 'diagramx': [3643, 5186, 1661, 5382], 'generators': [4103734078080, 127387560, 16, 87102720, 93409310300, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.8.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': ['4.A'], 'normal_contains': ['72.A'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '18432.q', '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': '40000.br'}
  • id: 63387166
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.B', '24.G'], 'contains': ['96.Q', '96.R', '96.V', '144.GP', '192.T'], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1525, -1, 191, -1], 'generators': [5606321851418, 11543, 16687, 127376056, 1313941668480, 87107887, 4103734078080, 174363851543], 'label': '18432.q.48.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.G', 'old_label': '48.f1', 'projective_image': '18432.q', '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': '192.1000'}
  • id: 63387167
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.H', '16.B'], 'contains': ['96.H', '96.I', '96.U', '144.GP', '192.Z'], 'core': '18432.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2429, -1, 344, -1], 'generators': [4103734078080, 6611, 11543, 5606321851418, 87107887, 1313941668480, 127376056, 16687], 'label': '18432.q.48.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '48.g1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.G', 'subgroup_fusion': None, 'weyl_group': '288.1024'}
  • id: 63387168
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.J'], 'contains': ['96.X', '144.GQ', '192.BI', '192.BJ', '192.BK', '192.DB', '192.DC', '192.DJ', '192.DO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4764, -1, 4187, -1], 'generators': [6227384421, 1313988496680, 4103734078087, 2789792409616, 5167, 2789705329920, 93409309459, 11536], 'label': '18432.q.48.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.H', 'old_label': '48.h1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.H', 'subgroup_fusion': None, 'weyl_group': '384.20164'}
  • id: 63387169
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.A', '24.D', '24.I'], 'contains': ['96.BE', '96.BG', '96.BJ', '144.JX', '192.BY'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [303, -1, 1348, -1], 'generators': [6227384421, 16, 5167, 1313941668480, 9709928549146, 11536, 843, 7], 'label': '18432.q.48.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.i1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.I', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387170
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.B', '24.D', '24.I'], 'contains': ['96.BE', '96.BI', '96.BJ', '144.JZ', '192.BZ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [171, -1, 1157, -1], 'generators': [5606275030426, 16, 7, 843, 11536, 4097506695141, 5167, 1313941668480], 'label': '18432.q.48.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.j1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.J', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387171
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.A', '24.C', '24.K'], 'contains': ['96.BF', '96.BG', '96.BH', '144.JW', '192.CA'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [425, -1, 1324, -1], 'generators': [6227384421, 16, 5167, 1313941668480, 11536, 8396027160338, 843, 7], 'label': '18432.q.48.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.k1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.K', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387172
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.B', '24.C', '24.K'], 'contains': ['96.BF', '96.BH', '96.BI', '144.JY', '192.CB'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [249, -1, 1131, -1], 'generators': [6920176419218, 16, 5167, 4097506695141, 1313941668480, 11536, 843, 7], 'label': '18432.q.48.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.l1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.L', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387173
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.A', '24.D', '24.K'], 'contains': ['96.K', '96.BE', '96.BF', '96.BG', '144.KA', '192.CC'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [629, -1, 1046, -1], 'generators': [6920176419218, 6227384421, 16, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.48.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.m1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.M', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387174
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.B', '24.D', '24.K'], 'contains': ['96.BE', '96.BF', '96.BI', '144.KB', '192.CD'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [354, -1, 1071, -1], 'generators': [16, 5167, 4097506695141, 1313941668480, 11536, 8396027160338, 843, 7], 'label': '18432.q.48.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.n1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.N', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387175
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.A', '24.C', '24.I'], 'contains': ['96.BG', '96.BH', '96.BJ', '144.KC', '192.CE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [205, -1, 1376, -1], 'generators': [6227384421, 16, 5606275030426, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.48.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.o1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.O', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387176
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.B'], 'contains': ['16.C', '16.D', '16.E', '24.J', '24.K', '32.A', '32.F'], 'core': '1152.A', 'coset_action_label': None, 'count': 8, 'diagramx': [3141, -1, 1227, -1], 'generators': [4103734078080, 6227384421, 16, 93409310300, 5167, 1313941668480, 11536, 8396027160338, 843, 7], 'label': '18432.q.8.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '8.b1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 63387177
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.B', '24.C', '24.I'], 'contains': ['96.BH', '96.BI', '96.BJ', '144.KD', '192.CF'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [143, -1, 1239, -1], 'generators': [16, 7, 843, 11536, 4097506695141, 5167, 1313941668480, 9709928549146], 'label': '18432.q.48.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.p1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.P', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387178
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.A', '24.B', '24.L'], 'contains': ['96.BE', '96.BH', '96.BK', '144.KF', '192.BT'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [475, -1, 1421, -1], 'generators': [16703, 4103734078080, 5606321857197, 127387560, 174363856680, 1313941668480, 87107903, 87107880], 'label': '18432.q.48.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.q1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.Q', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387179
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.A', '24.B', '24.M'], 'contains': ['96.BF', '96.BJ', '96.BK', '144.KE', '192.D', '192.BU'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [445, -1, 1189, -1], 'generators': [16, 87102720, 5606321841949, 5167, 2789792409600, 11536, 843, 7], 'label': '18432.q.48.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.r1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.R', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387180
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.A', '24.E', '24.N'], 'contains': ['96.L', '96.BG', '96.BK', '144.KG', '192.I', '192.BV'], 'core': '18432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1933, -1, 1759, -1], 'generators': [40284840, 6227384421, 16, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.48.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.s1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.S', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 63387181
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.B', '24.F', '24.N'], 'contains': ['96.BI', '96.BK', '144.KH', '192.L', '192.BW'], 'core': '18432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1150, -1, 1650, -1], 'generators': [40284840, 16, 5167, 4097506695141, 1313941668480, 11536, 843, 7], 'label': '18432.q.48.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.t1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.T', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 63387182
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.E', '24.F', '24.Q'], 'contains': ['96.M', '96.BK', '144.KI', '192.J', '192.K', '192.BX'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3586, -1, 1923, -1], 'generators': [40284840, 16, 5167, 1313941668480, 11536, 6354044781, 843, 7], 'label': '18432.q.48.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '48.u1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.U', 'subgroup_fusion': None, 'weyl_group': '384.20163'}
  • id: 63387183
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.D', '24.G', '24.L'], 'contains': ['96.Q', '96.BE', '96.BM', '144.KK', '192.BN'], 'core': '18432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [850, -1, 725, -1], 'generators': [87102727, 16703, 4103734078080, 5606321857197, 127382407, 1313941668480, 87107903, 174363851527], 'label': '18432.q.48.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.v1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.V', 'subgroup_fusion': None, 'weyl_group': '768.1087582'}
  • id: 63387184
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.C', '24.D', '24.M'], 'contains': ['96.BF', '96.BJ', '96.BM', '144.KJ', '192.G', '192.BM'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [379, -1, 858, -1], 'generators': [16, 5167, 9709881737629, 2789792409600, 11536, 4103646998400, 843, 7], 'label': '18432.q.48.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.w1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.W', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387185
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.C', '24.D', '24.N'], 'contains': ['96.BG', '96.BI', '96.BM', '144.KL', '192.A', '192.BO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [603, -1, 1263, -1], 'generators': [16, 7, 843, 11536, 4097506695141, 5167, 4103693803560, 1313941668480], 'label': '18432.q.48.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.x1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.X', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387186
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.C', '24.H', '24.L'], 'contains': ['96.BH', '96.BM', '144.KM', '192.BP'], 'core': '18432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [566, -1, 1017, -1], 'generators': [87102727, 16703, 4103734078080, 5606321851429, 127382407, 1313941668480, 87107903, 174363851527], 'label': '18432.q.48.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.y1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.Y', 'subgroup_fusion': None, 'weyl_group': '768.1087582'}
  • id: 63387187
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '9.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': ['18.A', '18.B', '18.C', '18.D', '18.E', '18.F', '18.G'], 'core': '72.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7208, -1, 7426, -1], 'generators': [4103734078080, 127387560, 87181926482, 16, 87102720, 5606321841949, 5167, 1313941668480, 11536, 11300123081647, 7], 'label': '18432.q.9.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '8640.bl'}
  • id: 63387188
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.G', '24.H', '24.O'], 'contains': ['96.R', '96.BM', '144.KN', '192.BQ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1455, -1, 561, -1], 'generators': [174363851527, 87102727, 87107903, 1313941668480, 127382407, 16703, 4103734078080, 5606321841949], 'label': '18432.q.48.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '48.z1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.Z', 'subgroup_fusion': None, 'weyl_group': '384.18158'}
  • id: 63387189
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.E', '24.F', '24.R'], 'contains': ['96.O', '96.S', '96.T', '96.BK', '96.BL', '144.KO', '192.B', '192.C', '192.F', '192.BL'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3428, -1, 1722, -1], 'generators': [127387560, 16, 87102720, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.48.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '48.ba1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BA', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387190
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.G', '24.H', '24.R'], 'contains': ['96.S', '96.T', '96.V', '96.BL', '96.BM', '144.KP', '192.E', '192.H', '192.BR'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2356, -1, 829, -1], 'generators': [127387560, 16, 5167, 1313941668480, 11536, 4103646998400, 843, 7], 'label': '18432.q.48.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '48.bb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BB', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63387191
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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.A', '24.J'], 'contains': ['96.BP', '96.BT', '96.BU', '144.LB', '192.O'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [918, -1, 1590, -1], 'generators': [4103734078080, 5606321847709, 5167, 1313941668480, 11536, 6314485090, 851, 40284847], 'label': '18432.q.48.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '48.bc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BC', 'subgroup_fusion': None, 'weyl_group': '384.18069'}
  • id: 63387192
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['12.B', '24.J'], 'contains': ['96.BQ', '96.BS', '96.BU', '144.KZ', '192.P'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2036, -1, 1549, -1], 'generators': [4103734078080, 5167, 1313941668480, 11536, 6314485093, 8396027160338, 40284847, 843], 'label': '18432.q.48.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '48.bd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BD', 'subgroup_fusion': None, 'weyl_group': '384.18069'}
  • id: 63387193
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['12.C', '24.J'], 'contains': ['96.BA', '96.BB', '96.BN', '96.BO', '96.BP', '96.BQ', '96.BR', '96.CA', '96.CB', '144.LC', '192.Q'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [275, -1, 1447, -1], 'generators': [4103734078080, 6227384402, 5167, 1313941668480, 11536, 8396027160338, 40284847, 843], 'label': '18432.q.48.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '48.be1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BE', 'subgroup_fusion': None, 'weyl_group': '384.18069'}
  • id: 63387194
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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.D', '24.J'], 'contains': ['96.BR', '96.BS', '96.BT', '144.LD', '192.R'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [940, -1, 1570, -1], 'generators': [4103734078080, 5606321847709, 6227384421, 5167, 1313941668480, 11536, 851, 40284847], 'label': '18432.q.48.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '48.bf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BF', 'subgroup_fusion': None, 'weyl_group': '384.18069'}
  • id: 63387195
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['16.C', '24.I', '24.K', '24.L'], 'contains': ['96.BE', '96.BH', '96.BW', '144.LP', '192.CJ'], 'core': '1152.A', 'coset_action_label': None, 'count': 12, 'diagramx': [535, -1, 1094, -1], 'generators': [4103734078080, 5606321851429, 87102736, 5167, 174363856703, 1313941668480, 11536, 40284847], 'label': '18432.q.48.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.bg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BG', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387196
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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.G', '16.D', '24.J'], 'contains': ['96.BC', '96.BD', '96.BP', '96.BS', '96.BV', '144.LQ', '192.X'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2060, -1, 590, -1], 'generators': [4103734078080, 16, 5167, 1313941668480, 11536, 174363856696, 8396027160338, 7], 'label': '18432.q.48.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '48.bh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BH', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 63387197
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['12.H', '16.C', '24.J'], 'contains': ['96.BQ', '96.BT', '96.BV', '144.LP', '192.Z'], 'core': '1152.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2322, -1, 1477, -1], 'generators': [4103734078080, 5606321851429, 87102736, 5167, 1313941668480, 11536, 40284847, 843], 'label': '18432.q.48.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '48.bi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BI', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 63387198
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.L', '24.P', '24.Q', '36.X', '48.BC'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1737, -1, 1597, -1], 'generators': [40284840, 4103734078080, 16, 5606321841949, 5167, 1313941668480, 11536, 6354044781, 843, 7], 'label': '18432.q.12.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.A', 'subgroup_fusion': None, 'weyl_group': '1536.408560345'}
  • id: 63387199
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['16.D', '24.K', '24.M'], 'contains': ['96.BF', '96.BW', '144.LQ', '192.U', '192.CK'], 'core': '1152.A', 'coset_action_label': None, 'count': 2, 'diagramx': [664, -1, 657, -1], 'generators': [4103734078080, 16, 5167, 1313941668480, 11536, 8396027160338, 843, 7], 'label': '18432.q.48.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '48.bj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 63387200
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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.I', '16.E', '24.J'], 'contains': ['96.Y', '96.Z', '96.BR', '96.BU', '96.BV', '144.LR', '192.BB'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2699, -1, 1684, -1], 'generators': [4103734078080, 6227384421, 87102736, 5167, 1313941668480, 860, 11536, 40284847], 'label': '18432.q.48.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '48.bk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BK', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 63387201
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['16.E', '24.I', '24.K', '24.N'], 'contains': ['96.BG', '96.BI', '96.BW', '144.LR', '192.BG', '192.CL'], 'core': '1152.A', 'coset_action_label': None, 'count': 12, 'diagramx': [896, -1, 1614, -1], 'generators': [4103734078080, 6227384421, 16, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.48.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '48.bl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BL', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387202
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '16.E'], 'contains': ['96.BX', '144.LR', '192.BD', '192.BI', '192.BK', '192.CM', '192.CO'], 'core': '1152.A', 'coset_action_label': None, 'count': 48, 'diagramx': [4152, -1, 2846, -1], 'generators': [4103734078080, 6227384421, 16, 93409309459, 5167, 1313941668480, 11536, 7], 'label': '18432.q.48.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BM', 'old_label': '48.bm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BM', 'subgroup_fusion': None, 'weyl_group': '384.20164'}
  • id: 63387203
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.I', '24.M', '24.P'], 'contains': ['96.BJ', '96.BW', '144.LS', '192.V', '192.CN'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [508, -1, 1217, -1], 'generators': [4103734078080, 16, 5606321841949, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.48.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.bn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BN', 'subgroup_fusion': None, 'weyl_group': '768.1087581'}
  • id: 63387204
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.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': ['24.L', '24.M', '24.N', '24.O', '24.P', '24.Q', '24.R'], 'contains': ['96.BK', '96.BL', '96.BM', '96.BW', '144.LT', '192.S', '192.W', '192.CG'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1015, -1, 1510, -1], 'generators': [4103734078080, 16, 87102720, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.48.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.bo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BO', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387205
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E', '24.T'], 'contains': ['96.BY', '144.MF', '192.CH', '192.CP', '192.CU', '192.CW'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5129, -1, 4896, -1], 'generators': [4103734078080, 127387576, 87102720, 93409309459, 19615115146917, 5167, 1313941668480, 11536], 'label': '18432.q.48.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.T', 'old_label': '48.bp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BP', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 63387206
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F', '24.T'], 'contains': ['96.BY', '144.ME', '192.CI', '192.CQ', '192.CS', '192.CT'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5156, -1, 5005, -1], 'generators': [87102727, 11536, 1313941668480, 5167, 127387576, 4103734078080, 93409310291, 19440678730917], 'label': '18432.q.48.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.T', 'old_label': '48.bq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BQ', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 63387207
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J', '24.T'], 'contains': ['96.BY', '144.MG', '192.BJ', '192.CM', '192.CR', '192.CV'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4861, -1, 4588, -1], 'generators': [4103734078080, 6227384421, 127387576, 87102720, 93409309459, 5167, 1313941668480, 11536], 'label': '18432.q.48.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.T', 'old_label': '48.br1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BR', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 63387208
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.E'], 'contains': ['96.CD', '144.OD', '192.CU', '192.CZ', '192.DK', '192.DQ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5330, -1, 4556, -1], 'generators': [127370903, 2789792421136, 16696, 87102720, 4103734083247, 19615115146917, 93409305135, 5183], 'label': '18432.q.48.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BS', 'old_label': '48.bs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BS', 'subgroup_fusion': None, 'weyl_group': '384.18221'}
  • id: 63387209
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.M', '24.O', '24.Q', '36.W', '48.BD'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2114, -1, 1542, -1], 'generators': [40284840, 7, 843, 6354044781, 11536, 1313941668480, 5167, 16, 4103734078080, 9709928549146], 'label': '18432.q.12.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.b1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.B', 'subgroup_fusion': None, 'weyl_group': '1536.408560345'}
  • id: 63387210
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.F'], 'contains': ['96.CE', '144.OC', '192.CQ', '192.CS', '192.DA', '192.DN', '192.DP'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5346, -1, 4735, -1], 'generators': [16696, 4103734083247, 5183, 87107887, 19440635185317, 127376056, 93409319531, 1313941680016], 'label': '18432.q.48.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BT', 'old_label': '48.bt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BT', 'subgroup_fusion': None, 'weyl_group': '384.20164'}
  • id: 63387211
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.J'], 'contains': ['96.CF', '144.OP', '192.CO', '192.CR', '192.DB', '192.DE', '192.DJ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4825, -1, 4396, -1], 'generators': [127370903, 6227384421, 2789792421136, 16, 93409309459, 4103734083247, 87091216, 7], 'label': '18432.q.48.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BU', 'old_label': '48.bu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BU', 'subgroup_fusion': None, 'weyl_group': '384.20164'}
  • id: 63387212
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.E', '24.U'], 'contains': ['96.CG', '144.OR', '192.CU', '192.DF', '192.DL', '192.DM'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5234, -1, 4683, -1], 'generators': [2789792421136, 16, 87102720, 4103734083247, 19615115146917, 93409305135, 127376056, 7], 'label': '18432.q.48.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.U', 'old_label': '48.bv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BV', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 63387213
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.F', '24.U'], 'contains': ['96.CG', '144.OQ', '192.CS', '192.CT', '192.DG', '192.DN', '192.DP'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5254, -1, 4750, -1], 'generators': [16, 4103734083247, 87107887, 19440635185317, 127376056, 93409319531, 7, 1313941680016], 'label': '18432.q.48.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.U', 'old_label': '48.bw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BW', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 63387214
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.J', '24.U'], 'contains': ['96.CG', '144.OS', '192.CO', '192.CV', '192.DC', '192.DI', '192.DO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4925, -1, 4573, -1], 'generators': [6227384421, 7, 127376056, 4103734083247, 93409309459, 87102720, 16, 2789792421136], 'label': '18432.q.48.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.U', 'old_label': '48.bx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BX', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 63387215
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.B', '16.D'], 'contains': ['128.A', '192.T', '192.U', '256.B', '256.D'], 'core': '18432.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3137, -1, 8, -1], 'generators': [4103734078080, 11543, 1313941668480, 8396027160338, 93409319531, 843, 16687], 'label': '18432.q.64.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.A', 'old_label': '64.a1', 'projective_image': '18432.q', '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': '288.1024'}
  • id: 63387216
    {'ambient': '18432.q', '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.D', '32.A'], 'contains': ['128.B', '192.X', '192.BA', '256.A', '256.D'], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3214, -1, 50, -1], 'generators': [5606234750738, 16, 93409310300, 5167, 11536, 843, 7], 'label': '18432.q.64.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.A', 'old_label': '64.b1', 'projective_image': '18432.q', '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': '192.955'}
  • id: 63387217
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.B', '16.C', '32.A'], 'contains': ['128.B', '192.Y', '192.Z', '256.B'], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3345, -1, 81, -1], 'generators': [4103734078080, 93409304523, 40279680, 1313941668480, 5606321841938, 87091200, 843], 'label': '18432.q.64.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.A', 'old_label': '64.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.C', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
  • id: 63387218
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.A', '16.E', '32.A'], 'contains': ['128.B', '192.BB', '192.BC', '192.BD', '256.C', '256.E'], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3868, -1, 1689, -1], 'generators': [6227384421, 16, 93409310300, 5167, 11536, 843, 7], 'label': '18432.q.64.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.A', 'old_label': '64.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.D', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
  • id: 63387219
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.A', '16.E'], 'contains': ['128.C', '192.BG', '192.BH', '192.BI', '256.C', '256.E'], 'core': '18432.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3947, -1, 1977, -1], 'generators': [4103734078080, 6227384421, 93409304532, 16, 1313941668480, 843, 7], 'label': '18432.q.64.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.E', 'old_label': '64.e1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.E', 'subgroup_fusion': None, 'weyl_group': '288.1026'}
  • id: 63387220
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.A', '24.B', '24.C', '24.D', '24.I', '24.K', '24.L', '24.M', '24.N', '36.Y', '48.BE'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [511, -1, 1342, -1], 'generators': [40284840, 7, 843, 11536, 1313941668480, 5167, 16, 6227384421, 4103734078080, 9709928549146], 'label': '18432.q.12.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.C', 'subgroup_fusion': None, 'weyl_group': '1536.408560345'}
  • id: 63387221
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B', '32.E'], 'contains': ['128.E', '192.CH', '192.CI'], 'core': '1152.A', 'coset_action_label': None, 'count': 32, 'diagramx': [4982, -1, 4610, -1], 'generators': [4103734078080, 93409310292, 19615115146917, 5167, 1313941668480, 860, 11536], 'label': '18432.q.64.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.E', 'old_label': '64.f1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.F', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
  • id: 63387222
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.C', '16.D', '32.F'], 'contains': ['128.E', '192.CJ', '192.CK', '256.A', '256.B'], 'core': '1152.A', 'coset_action_label': None, 'count': 32, 'diagramx': [3369, -1, 439, -1], 'generators': [4103734078080, 5167, 1313941668480, 11536, 93485161460, 8396027160338, 843], 'label': '18432.q.64.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.F', 'old_label': '64.g1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.G', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 63387223
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.E', '32.E', '32.F', '32.G'], 'contains': ['128.E', '192.CL', '192.CM', '256.C'], 'core': '1152.A', 'coset_action_label': None, 'count': 16, 'diagramx': [4102, -1, 1826, -1], 'generators': [4103734078080, 6227384421, 5167, 1313941668480, 93528701300, 11536, 851], 'label': '18432.q.64.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '64.h1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.H', 'subgroup_fusion': None, 'weyl_group': '1152.157849'}
  • id: 63387224
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B'], 'contains': ['128.G', '192.CZ', '192.DA'], 'core': '18432.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [7223, -1, 4035, -1], 'generators': [10092, 2615428576220, 4103647003567, 1313988485176, 19615115146917, 11543, 16687], 'label': '18432.q.64.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.I', 'old_label': '64.i1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.I', 'subgroup_fusion': None, 'weyl_group': '288.1025'}
  • id: 63387225
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.A', '32.H'], 'contains': ['128.H', '192.DD', '192.DE', '256.E'], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4224, -1, 3988, -1], 'generators': [127370903, 6227384421, 93409304532, 16, 87091216, 843, 7], 'label': '18432.q.64.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.H', 'old_label': '64.j1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.J', 'subgroup_fusion': None, 'weyl_group': '576.8652'}
  • id: 63387226
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.B', '32.I'], 'contains': ['128.I', '192.DF', '192.DG'], 'core': '18432.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [6086, -1, 4473, -1], 'generators': [2789705318416, 15860, 16, 19615115146917, 2615428585451, 4103606707223, 7], 'label': '18432.q.64.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.I', 'old_label': '64.k1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.K', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
  • id: 63387227
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '64.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.A', '32.I'], 'contains': ['128.I', '192.DH', '192.DI', '256.E'], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4958, -1, 4013, -1], 'generators': [6227384421, 6611, 127387560, 87102720, 11520, 5160, 93409319531], 'label': '18432.q.64.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.I', 'old_label': '64.l1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.L', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
  • id: 63387228
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.R', '24.S', '36.BA', '36.BB', '36.BC'], 'contains': ['144.DM', '144.DN', '144.EE', '144.EF', '144.JQ', '144.JV', '144.KO', '144.KP', '144.LO', '144.LT'], 'core': '72.A', 'coset_action_label': None, 'count': 1, 'diagramx': [4411, 5186, 4641, 5382], 'generators': [4103734078080, 127387560, 16, 87102720, 5167, 1313941668480, 11536, 7], 'label': '18432.q.72.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': ['8.A'], 'normal_contains': ['1152.A'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.A', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 63387229
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.B'], 'contains': ['144.W', '144.X', '144.BN', '144.BP', '144.BR', '144.MK', '144.MM', '144.MO', '144.NE', '144.NG', '144.NI'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6963, -1, 6731, -1], 'generators': [127387560, 87102720, 20835531390117, 180591240241, 5167, 11520, 2789792409600, 7], 'label': '18432.q.72.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '72.b1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.B', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387230
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.B'], 'contains': ['144.W', '144.Y', '144.BO', '144.BQ', '144.BS', '144.ML', '144.MN', '144.MP', '144.NF', '144.NH', '144.NJ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7018, -1, 6772, -1], 'generators': [127387560, 3923142859457, 87102720, 20835531390117, 5167, 11520, 2789792409600, 7], 'label': '18432.q.72.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '72.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.C', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387231
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.B'], 'contains': ['24.N', '24.O', '24.P', '36.Z', '48.BF'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2047, -1, 1570, -1], 'generators': [40284840, 4103734078080, 6227384421, 16, 5606321841949, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.12.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.D', 'subgroup_fusion': None, 'weyl_group': '1536.408560345'}
  • id: 63387232
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.D'], 'contains': ['144.BA', '144.BW', '144.BX', '144.MQ', '144.NC'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5429, -1, 7378, -1], 'generators': [11219135529616, 6227395321, 4103606723880, 7, 4103646998400, 11520, 5167, 1313941668480], 'label': '18432.q.72.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.D', 'old_label': '72.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.D', 'subgroup_fusion': None, 'weyl_group': '128.513'}
  • id: 63387233
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.E'], 'contains': ['144.BB', '144.BY', '144.BZ', '144.MR', '144.ND'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5544, -1, 7480, -1], 'generators': [4097506694537, 4103606723880, 7, 4103646998400, 11520, 5167, 1313941668480, 11219135523247], 'label': '18432.q.72.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '72.e1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.E', 'subgroup_fusion': None, 'weyl_group': '128.513'}
  • id: 63387234
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.B'], 'contains': ['144.BJ', '144.BK', '144.BO', '144.BP', '144.BR', '144.MU', '144.MV', '144.MY', '144.NA'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6884, -1, 6944, -1], 'generators': [20835531393818, 4103734089600, 4103606712376, 5167, 2789792409600, 3923142870961, 4103646998400, 7], 'label': '18432.q.72.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '72.f1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.F', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387235
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.B'], 'contains': ['144.BJ', '144.BL', '144.BN', '144.BQ', '144.BS', '144.MW', '144.MX', '144.MZ', '144.NB'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7311, -1, 6966, -1], 'generators': [180591228737, 20835531393818, 4103734089600, 4103606712376, 5167, 2789792409600, 4103646998400, 7], 'label': '18432.q.72.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '72.g1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.G', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387236
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.D'], 'contains': ['144.BT', '144.BW', '144.BX', '144.MS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5466, -1, 7418, -1], 'generators': [11219135529616, 4103606723880, 4103734078096, 5167, 4097506694537, 7, 1313941668480, 4103646998400], 'label': '18432.q.72.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.D', 'old_label': '72.h1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.H', 'subgroup_fusion': None, 'weyl_group': '128.513'}
  • id: 63387237
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.E'], 'contains': ['144.BU', '144.BY', '144.BZ', '144.MT'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5606, -1, 7504, -1], 'generators': [6227395321, 4103606723880, 11219135523247, 4103734078096, 5167, 7, 1313941668480, 4103646998400], 'label': '18432.q.72.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '72.i1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.I', 'subgroup_fusion': None, 'weyl_group': '128.513'}
  • id: 63387238
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.F'], 'contains': ['144.CA', '144.CB', '144.CE', '144.CF', '144.CG', '144.CJ', '144.CM', '144.NK', '144.NL', '144.NM', '144.NN'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9850, -1, 9843, -1], 'generators': [87181935962, 1313941680007, 11300123081647, 1314028759696, 127387560, 16703, 4103734078080, 6920263519898], 'label': '18432.q.72.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '72.j1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.J', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387239
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.F'], 'contains': ['144.CC', '144.CD', '144.CE', '144.CF', '144.CG', '144.CL', '144.CM'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9784, -1, 9754, -1], 'generators': [6920263510429, 16703, 1313941680007, 11300123076480, 1482078131293, 127387560, 1314028759696, 4103734078080], 'label': '18432.q.72.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '72.k1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.K', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387240
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.H'], 'contains': ['144.CK', '144.CO', '144.CP'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7520, -1, 8872, -1], 'generators': [5606321851418, 1482078140762, 1313941680007, 11300046513967, 1314028759696, 127387560, 16703, 4103734078080], 'label': '18432.q.72.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.H', 'old_label': '72.l1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.L', 'subgroup_fusion': None, 'weyl_group': '256.4741'}
  • id: 63387241
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.H'], 'contains': ['144.CN', '144.CO', '144.CP'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7491, -1, 8905, -1], 'generators': [6920263510429, 1482078140762, 1313941680007, 11300046513967, 127387560, 1314028759696, 16703, 4103734078080], 'label': '18432.q.72.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.H', 'old_label': '72.m1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.M', 'subgroup_fusion': None, 'weyl_group': '256.4741'}
  • id: 63387242
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B', '6.A'], 'contains': ['24.S', '36.BA', '48.BP', '48.BS', '48.BV'], 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5226, -1, 4646, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 93409309459, 19615115146917, 5167, 1313941668480, 11536, 7], 'label': '18432.q.12.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '12.e1', 'projective_image': '18432.q', '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': '2880.du'}
  • id: 63387243
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.A', '36.B', '36.BA'], 'contains': ['144.N', '144.W', '144.BJ', '144.DA', '144.DD', '144.DM', '144.EV', '144.EY', '144.NO', '144.NQ', '144.NR', '144.NW', '144.NX', '144.OA', '144.OQ', '144.OR', '144.OT'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6286, -1, 6131, -1], 'generators': [127387560, 16, 87102720, 20835531390117, 4103734083247, 1313941668480, 5160, 11536], 'label': '18432.q.72.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.n1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.N', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387367
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['32.B', '48.B', '48.BA'], 'contains': ['192.BE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3530, -1, 1940, -1], 'generators': [127387560, 16, 87102720, 5167, 11536, 843, 7], 'label': '18432.q.96.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.A', 'old_label': '96.o1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.O', 'subgroup_fusion': None, 'weyl_group': '288.1036'}
  • id: 63387244
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.B', '36.C', '36.BC'], 'contains': ['144.O', '144.P', '144.X', '144.Y', '144.BK', '144.BL', '144.DG', '144.DH', '144.DM', '144.EX', '144.FB', '144.NP', '144.NY', '144.OS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6566, -1, 5913, -1], 'generators': [6227384421, 7, 4103734083247, 127382407, 87102720, 16, 4103734089616, 1313941668480], 'label': '18432.q.72.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.o1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.O', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387245
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.A', '36.C', '36.BA'], 'contains': ['144.DB', '144.DC', '144.DM', '144.EY', '144.EZ', '144.NR', '144.NS', '144.NZ', '144.OT'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6195, -1, 6114, -1], 'generators': [127387560, 5160, 4103734083247, 87102720, 16, 11536, 1313941668480, 19440635185317], 'label': '18432.q.72.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.p1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.P', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387246
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.A', '36.BC'], 'contains': ['144.Q', '144.R', '144.Z', '144.BM', '144.DI', '144.DJ', '144.DM', '144.FA', '144.FB'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4733, -1, 5409, -1], 'generators': [16, 7, 6227390173, 4103734083247, 127382407, 87102720, 4103734089616, 1313941668480], 'label': '18432.q.72.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.q1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Q', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387247
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.D', '36.E', '36.BC'], 'contains': ['144.S', '144.T', '144.BA', '144.BB', '144.BT', '144.BU', '144.DG', '144.DI', '144.DN', '144.FE', '144.FG', '144.NT', '144.OB', '144.OP'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5362, -1, 6098, -1], 'generators': [6227384421, 5160, 87107887, 5183, 4103734083247, 127382407, 4103734089616, 1313941668480], 'label': '18432.q.72.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '72.r1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.R', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 63387248
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.BC'], 'contains': ['144.U', '144.V', '144.BC', '144.BV', '144.DH', '144.DJ', '144.DN', '144.FF', '144.FG'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4566, -1, 5172, -1], 'generators': [127382407, 5160, 87107887, 5183, 6227390173, 4103734083247, 4103734089616, 1313941668480], 'label': '18432.q.72.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '72.s1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.S', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 63387249
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.K'], 'contains': ['144.BE', '144.BF', '144.CW', '144.CX', '144.DQ', '144.DS', '144.DU', '144.FH', '144.FI', '144.FN', '144.FO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9080, -1, 9384, -1], 'generators': [4103734078080, 127387560, 12694932195247, 5176, 8396027160338, 87181920722, 1313941673647, 1313941680016], 'label': '18432.q.72.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '72.t1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.T', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387250
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.M'], 'contains': ['144.DR', '144.DV', '144.DX'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8823, -1, 7860, -1], 'generators': [8396027160346, 11300079536047, 1313941680016, 1313941673647, 5176, 87258503650, 127387560, 4103734078080], 'label': '18432.q.72.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.M', 'old_label': '72.u1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.U', 'subgroup_fusion': None, 'weyl_group': '256.4741'}
  • id: 63387251
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.K'], 'contains': ['144.DS', '144.DT', '144.DU', '144.FJ', '144.FK', '144.FL', '144.FM'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9185, -1, 9257, -1], 'generators': [4103734078080, 127387560, 12694932195247, 8396027166106, 5176, 87181920722, 1313941673647, 1313941680016], 'label': '18432.q.72.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '72.v1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.V', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387252
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.M'], 'contains': ['144.DV', '144.DW', '144.DX'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8770, -1, 7827, -1], 'generators': [11300079536047, 4103734078080, 127387560, 87258503650, 8396027166098, 5176, 1313941673647, 1313941680016], 'label': '18432.q.72.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.M', 'old_label': '72.w1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.W', 'subgroup_fusion': None, 'weyl_group': '256.4741'}
  • id: 63387253
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.B', '6.A'], 'contains': ['24.S', '36.BA', '48.BQ', '48.BT', '48.BW'], 'core': '72.A', 'coset_action_label': None, 'count': 2, 'diagramx': [5251, -1, 4735, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 20835531390117, 93409310300, 5167, 1313941668480, 11536, 7], 'label': '18432.q.12.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '12.f1', 'projective_image': '18432.q', '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': '86400.o'}
  • id: 63387254
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.P'], 'contains': ['144.DO', '144.DP', '144.DT', '144.DW', '144.DY', '144.EA', '144.EB', '144.FP', '144.FR', '144.FV', '144.FW', '144.FY', '144.GA', '144.GD', '144.GE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8476, -1, 7983, -1], 'generators': [127387560, 87102736, 4103734089616, 5167, 180591240257, 2789792409600, 4103734078087, 18301133928218], 'label': '18432.q.72.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '72.x1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.X', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387255
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.P'], 'contains': ['144.DO', '144.DP', '144.DQ', '144.DR', '144.DY', '144.DZ', '144.EA', '144.FQ', '144.FS', '144.FT', '144.FU', '144.FX', '144.FZ', '144.GB', '144.GC'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8361, -1, 8038, -1], 'generators': [18301133924517, 127387560, 87102736, 4103734089616, 5167, 180591240257, 2789792409600, 4103734078087], 'label': '18432.q.72.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '72.y1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Y', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387256
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.BA'], 'contains': ['144.M', '144.BD', '144.BG', '144.DA', '144.DC', '144.DZ', '144.EC', '144.EF', '144.NQ', '144.NS', '144.NU', '144.NV', '144.NX', '144.NZ', '144.OC', '144.OD', '144.OE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5976, -1, 5737, -1], 'generators': [127387560, 87102720, 20835531390117, 4103734083247, 5183, 1313941668480, 11536, 7], 'label': '18432.q.72.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '72.z1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Z', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387257
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.BA'], 'contains': ['144.DB', '144.DD', '144.EB', '144.EC', '144.EF', '144.NR', '144.NZ', '144.OA', '144.OE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6068, -1, 5854, -1], 'generators': [127387560, 87102720, 4103734083247, 5183, 1313941668480, 19440635185317, 11536, 7], 'label': '18432.q.72.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '72.ba1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BA', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387258
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.F', '36.I', '36.K'], 'contains': ['144.BH', '144.CA', '144.CC', '144.EI', '144.EM', '144.EQ', '144.FH', '144.FJ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9538, -1, 9548, -1], 'generators': [8396027166106, 23, 1313941680016, 1313941673647, 87181920722, 12694932195247, 127387560, 4103734078080], 'label': '18432.q.72.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BB', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387259
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.F', '36.J', '36.K'], 'contains': ['144.BI', '144.CB', '144.CD', '144.EI', '144.EM', '144.ER', '144.FI', '144.FK'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9485, -1, 9510, -1], 'generators': [8396027160338, 23, 1313941673647, 87181920722, 11300123081647, 127387560, 1313941680016, 4103734078080], 'label': '18432.q.72.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BC', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387260
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.F', '36.I', '36.L'], 'contains': ['144.CE', '144.EI', '144.EP', '144.EQ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9637, -1, 9624, -1], 'generators': [23, 1313941680016, 1313941673647, 87181920722, 12694932195247, 127387560, 4103734078080, 5606321847717], 'label': '18432.q.72.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BD', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387261
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.F', '36.J', '36.L'], 'contains': ['144.CF', '144.EI', '144.EP', '144.ER'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9606, -1, 9594, -1], 'generators': [23, 1313941680016, 1313941673647, 87181920722, 11300123081647, 127387560, 4103734078080, 5606321841949], 'label': '18432.q.72.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.be1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BE', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387262
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.G', '36.I', '36.K'], 'contains': ['144.EM', '144.EO', '144.EQ', '144.FL', '144.FN'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9460, -1, 9451, -1], 'generators': [8396027160338, 23, 1313941680016, 1313941673647, 87181920722, 12694932195247, 127387560, 4103734078080], 'label': '18432.q.72.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BF', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387263
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.G', '36.J', '36.K'], 'contains': ['144.EM', '144.EO', '144.ER', '144.FM', '144.FO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9326, -1, 9422, -1], 'generators': [8396027166106, 23, 1313941680016, 1313941673647, 87181920722, 11300123081647, 127387560, 4103734078080], 'label': '18432.q.72.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BG', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387264
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.C', '6.B'], 'contains': ['24.G', '24.H', '24.L', '24.O', '24.R', '36.BB', '48.BH'], 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2088, -1, 1308, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 5606321841949, 5167, 1313941668480, 11536, 174363856696, 7], 'label': '18432.q.12.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.g1', 'projective_image': '18432.q', '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': '768.1087582'}
  • id: 63387265
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.G', '36.I', '36.L'], 'contains': ['144.EO', '144.EP', '144.EQ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9557, -1, 9530, -1], 'generators': [23, 1313941673647, 87181920722, 12694932195247, 127387560, 1313941680016, 4103734078080, 5606321841949], 'label': '18432.q.72.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BH', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387266
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.G', '36.J', '36.L'], 'contains': ['144.EO', '144.EP', '144.ER'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9512, -1, 9480, -1], 'generators': [23, 1313941680016, 1313941673647, 87181920722, 11300123081647, 127387560, 4103734078080, 5606321847717], 'label': '18432.q.72.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BI', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387267
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.A', '36.P'], 'contains': ['144.EG', '144.EH', '144.EV', '144.EZ', '144.FA', '144.FQ', '144.FR', '144.FS', '144.FW'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8130, -1, 7764, -1], 'generators': [127387560, 4103734089616, 5167, 180591240257, 2789792409600, 4103646998416, 18301133928218, 7], 'label': '18432.q.72.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.bj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BJ', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387268
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.BK', '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': ['36.A', '36.B', '36.O'], 'contains': ['144.BN', '144.BO', '144.EV', '144.EY', '144.FB', '144.OI', '144.OJ', '144.OK', '144.OO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6759, -1, 6917, -1], 'generators': [127387560, 20835531393818, 4103734089616, 5167, 2789792409600, 3923142870961, 4103646998416, 7], 'label': '18432.q.72.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.bk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BK', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387269
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.B', '36.F', '36.P'], 'contains': ['144.BP', '144.BQ', '144.CG', '144.EI', '144.EJ', '144.EV', '144.EX', '144.FP', '144.FT', '144.OF', '144.OH', '144.OL'], 'core': '18432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8104, -1, 7625, -1], 'generators': [127387560, 4103734089616, 5167, 2789792409600, 3923142870977, 4103646998416, 18301133928218, 7], 'label': '18432.q.72.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.bl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BL', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387270
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.F', '36.G', '36.R'], 'contains': ['144.CH', '144.CJ', '144.CL', '144.EK', '144.EM', '144.EP', '144.EW', '144.EX'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9206, -1, 9342, -1], 'generators': [6227384421, 127382400, 127382423, 4103734089616, 4103734083247, 87102720, 1313941668480, 5606321847717], 'label': '18432.q.72.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BM', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387271
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.H', '36.R'], 'contains': ['144.CI', '144.CK', '144.CN', '144.EL', '144.EN', '144.EU', '144.EW', '144.FA'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7629, -1, 8765, -1], 'generators': [87102720, 127382400, 127382423, 6227390173, 4103734083247, 4103734089616, 1313941668480, 5606321841949], 'label': '18432.q.72.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '72.bn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BN', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387272
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.B', '36.C', '36.T'], 'contains': ['144.BR', '144.BS', '144.EX', '144.EY', '144.OM', '144.ON'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7331, -1, 7110, -1], 'generators': [127387560, 20835531393818, 4103734089616, 5167, 2789792409600, 3923142870977, 4103646998416, 7], 'label': '18432.q.72.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.bo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BO', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387273
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.C', '36.G', '36.P'], 'contains': ['144.EO', '144.ES', '144.EX', '144.EZ', '144.FU', '144.FV'], 'core': '18432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8402, -1, 8020, -1], 'generators': [18301133924517, 127387560, 4103734089616, 5167, 2789792409600, 3923142870977, 4103646998416, 7], 'label': '18432.q.72.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.bp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BP', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387274
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.F', '36.G', '36.U'], 'contains': ['144.CM', '144.EQ', '144.ER', '144.EX'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9578, -1, 9568, -1], 'generators': [127387560, 11219048432047, 87102720, 4103734089616, 6227383801, 5167, 1313941668480, 7], 'label': '18432.q.72.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BQ', 'subgroup_fusion': None, 'weyl_group': '256.16883'}
  • id: 63387275
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.A', '4.B', '6.A', '32.E', '32.I'], 'core': '2.A', 'coset_action_label': None, 'count': 1, 'diagramx': [4878, 8294, 4568, 8606], 'generators': [11536, 16, 843, 127387560, 4103734078080, 19615115146917, 5167, 7, 1313941668480, 87102720, 93409310300, 6227384421], 'label': '18432.q.2.A', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.A', 'subgroup_fusion': None, 'weyl_group': '40000.br'}
  • id: 63387276
    {'ambient': '18432.q', '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': ['4.C', '6.B'], 'contains': ['24.M', '24.P', '24.R', '36.BB', '48.G', '48.BI'], 'core': '72.A', 'coset_action_label': None, 'count': 2, 'diagramx': [2211, -1, 1446, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 5606321841949, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.12.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '12.h1', 'projective_image': '18432.q', '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': None}
  • id: 63387277
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.BR', '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': ['36.A', '36.C', '36.O'], 'contains': ['144.EY', '144.EZ', '144.FB', '144.OG'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6471, -1, 6985, -1], 'generators': [127387560, 20835531390117, 4103734089616, 5167, 2789792409600, 3923142870961, 4103646998416, 7], 'label': '18432.q.72.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.br1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BR', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387278
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.BS', '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': ['36.A', '36.H', '36.T'], 'contains': ['144.CO', '144.EY', '144.FA'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7466, -1, 7603, -1], 'generators': [127387560, 20835531390117, 4103734089616, 5167, 180591240257, 2789792409600, 4103646998416, 7], 'label': '18432.q.72.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.bs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BS', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387433
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3211, -1, 465, -1], 'generators': [127370903, 16, 87096383, 5606321841949, 1313941668480, 5160, 4103734094783], 'label': '18432.q.144.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CJ', 'old_label': '144.b1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.B', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387279
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.H', '36.V'], 'contains': ['144.CP', '144.ET', '144.FA'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7565, -1, 8466, -1], 'generators': [4097506694521, 127387560, 87102720, 4103734089616, 5167, 1313941668480, 11219135529616, 7], 'label': '18432.q.72.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '72.bt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BT', 'subgroup_fusion': None, 'weyl_group': '256.5695'}
  • id: 63387280
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.I', '36.J', '36.P'], 'contains': ['144.EG', '144.EI', '144.EO', '144.FC', '144.FE', '144.FX', '144.FY', '144.GB', '144.GD'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8663, -1, 8274, -1], 'generators': [4103606723880, 4103734089616, 5167, 2789792409600, 3923142870977, 4103646998416, 18301133928218, 7], 'label': '18432.q.72.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BU', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387281
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.P'], 'contains': ['144.EH', '144.EJ', '144.ES', '144.FC', '144.FF', '144.FZ', '144.GA', '144.GC', '144.GE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8567, -1, 8119, -1], 'generators': [18301133924517, 4103606723880, 4103734089616, 5167, 180591240257, 2789792409600, 4103646998416, 7], 'label': '18432.q.72.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.bv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BV', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387282
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.I', '36.J', '36.R'], 'contains': ['144.CQ', '144.CS', '144.CU', '144.EL', '144.EM', '144.EP', '144.FD', '144.FE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8157, -1, 8828, -1], 'generators': [6227384421, 127387567, 87107887, 4103734089616, 4103734083247, 127387576, 1313941668480, 5606321841949], 'label': '18432.q.72.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BW', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387283
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.R'], 'contains': ['144.CR', '144.CT', '144.CV', '144.EK', '144.EN', '144.EU', '144.FD', '144.FF'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7888, -1, 8618, -1], 'generators': [127387576, 127387567, 87107887, 6227390173, 4103734089616, 4103734083247, 1313941668480, 5606321847717], 'label': '18432.q.72.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '72.bx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BX', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387284
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.D', '36.I', '36.U'], 'contains': ['144.BW', '144.EQ', '144.FE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8073, -1, 7782, -1], 'generators': [4103606723880, 11219048432047, 4103734089616, 6227383801, 5167, 1313941668480, 4103646998400, 7], 'label': '18432.q.72.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.by1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BY', 'subgroup_fusion': None, 'weyl_group': '512.51574'}
  • id: 63387285
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.E', '36.J', '36.U'], 'contains': ['144.BY', '144.ER', '144.FE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8043, -1, 7802, -1], 'generators': [4103606723880, 11219048438416, 4103734089616, 6227383801, 5167, 1313941668480, 4103646998400, 7], 'label': '18432.q.72.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.bz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BZ', 'subgroup_fusion': None, 'weyl_group': '512.51574'}
  • id: 63387286
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.D', '36.E', '36.V'], 'contains': ['144.BX', '144.BZ', '144.ET', '144.FE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6165, -1, 7648, -1], 'generators': [4103606723880, 4103734089616, 6227383801, 5167, 1313941668480, 11219135523247, 4103646998400, 7], 'label': '18432.q.72.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '72.ca1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CA', 'subgroup_fusion': None, 'weyl_group': '256.1529'}
  • id: 63387287
    {'ambient': '18432.q', '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': ['4.A', '6.B'], 'contains': ['24.E', '24.F', '24.N', '24.Q', '24.R', '36.BC', '48.A', '48.BK'], 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3465, -1, 1816, -1], 'generators': [11536, 16, 843, 127387560, 4103734078080, 5167, 7, 1313941668480, 87102720, 6227384421], 'label': '18432.q.12.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.i1', 'projective_image': '18432.q', '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': '768.1087581'}
  • id: 63387288
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Y'], 'contains': ['144.GZ', '144.HA', '144.HD', '144.HF', '144.HH', '144.HI', '144.HL', '144.HN', '144.HQ', '144.HS', '144.HT', '144.HV', '144.HX', '144.HY', '144.IA'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2036, -1, 2916, -1], 'generators': [6227384421, 4103693803560, 5167, 1313941668480, 9709928549146, 11536, 4103734078087, 4103734078096], 'label': '18432.q.72.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.cb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CB', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387289
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Y'], 'contains': ['144.HB', '144.HC', '144.HE', '144.HG', '144.HJ', '144.HK', '144.HM', '144.HO', '144.HP', '144.HR', '144.HU', '144.HW', '144.HX', '144.HY', '144.IB'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2071, -1, 3324, -1], 'generators': [4103693803560, 5606275030426, 5167, 4097506695141, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.72.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.cc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CC', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387290
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.CD', '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': ['36.R'], 'contains': ['144.CH', '144.CI', '144.CL', '144.CN', '144.CQ', '144.CR', '144.CU', '144.CV', '144.IH', '144.II', '144.IL', '144.IM', '144.IN', '144.IP', '144.IQ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7839, -1, 8729, -1], 'generators': [127387576, 87102720, 5606321841949, 5167, 4097506695141, 1313941668480, 11536, 4103606723887], 'label': '18432.q.72.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '72.cd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CD', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387291
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.R'], 'contains': ['144.CH', '144.CI', '144.CJ', '144.CK', '144.CQ', '144.CR', '144.CS', '144.CT', '144.II', '144.IJ', '144.IK', '144.IL', '144.IN', '144.IO', '144.IP'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7780, -1, 8702, -1], 'generators': [9709881737629, 127387576, 4103606723887, 11536, 4097506695141, 5167, 87102720, 1313941668480], 'label': '18432.q.72.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '72.ce1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CE', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387292
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Y'], 'contains': ['144.GR', '144.GT', '144.GX', '144.GY', '144.HH', '144.HJ', '144.HN', '144.HO', '144.IW', '144.IZ', '144.JB', '144.JE', '144.JG', '144.JJ', '144.JL'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1245, -1, 3015, -1], 'generators': [40284840, 5606275030426, 5167, 4097506695141, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.72.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.cf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387293
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Y'], 'contains': ['144.GS', '144.GU', '144.GV', '144.GW', '144.HI', '144.HK', '144.HL', '144.HM', '144.IW', '144.IY', '144.IZ', '144.JF', '144.JH', '144.JI', '144.JK'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1539, -1, 3390, -1], 'generators': [40284840, 5167, 4097506695141, 1313941668480, 9709928549146, 11536, 4103734078087, 4103734078096], 'label': '18432.q.72.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.cg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CG', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387294
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.BC'], 'contains': ['144.C', '144.I', '144.O', '144.R', '144.S', '144.V', '144.BK', '144.BM', '144.BT', '144.BV', '144.GH', '144.GQ', '144.IA', '144.IC', '144.ID', '144.IF', '144.JM', '144.JP', '144.JQ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4658, -1, 5274, -1], 'generators': [4103606723880, 6227384421, 87102720, 5167, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.72.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '72.ch1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CH', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387311
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.M', '36.N', '36.P'], 'contains': ['144.DP', '144.DR', '144.DW', '144.EG', '144.EJ', '144.ES', '144.LG', '144.LL', '144.LV', '144.LX', '144.MC'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8745, -1, 7917, -1], 'generators': [18301133924517, 4103734078080, 180703353737, 87102736, 5167, 1313941668480, 11536, 7], 'label': '18432.q.72.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.cw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CW', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387295
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.BC'], 'contains': ['144.P', '144.Q', '144.T', '144.U', '144.BL', '144.BM', '144.BU', '144.BV', '144.IB', '144.IC', '144.IE', '144.IG', '144.JN', '144.JO', '144.JQ'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4492, -1, 5118, -1], 'generators': [4103606723880, 87102720, 5167, 4097506695141, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.72.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '72.ci1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CI', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387296
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.BB'], 'contains': ['144.A', '144.B', '144.F', '144.G', '144.H', '144.L', '144.IO', '144.IR', '144.IS', '144.IV', '144.IX', '144.IY', '144.JC', '144.JD', '144.JR', '144.JU', '144.JV'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2974, -1, 752, -1], 'generators': [16703, 4103734078080, 127387560, 16, 87102720, 5606321841949, 1313941668480, 5160], 'label': '18432.q.72.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '72.cj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CJ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387297
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.BB'], 'contains': ['144.IQ', '144.IR', '144.IT', '144.IU', '144.JA', '144.JB', '144.JC', '144.JD', '144.JS', '144.JT', '144.JV'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2868, -1, 875, -1], 'generators': [16703, 5160, 1313941668480, 87102720, 16, 127387560, 4103734078080, 5606321847717], 'label': '18432.q.72.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '72.ck1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CK', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387298
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '6.A'], 'contains': ['24.S', '36.BC', '48.C', '48.H', '48.BM', '48.BR', '48.BU', '48.BX'], 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4729, -1, 4422, -1], 'generators': [4103734078080, 6227384421, 127387560, 16, 87102720, 93409309459, 5167, 1313941668480, 11536, 7], 'label': '18432.q.12.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '12.j1', 'projective_image': '18432.q', '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': None}
  • id: 63387299
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.A', '36.Y'], 'contains': ['144.GR', '144.GS', '144.GV', '144.GX', '144.HP', '144.HR', '144.HT', '144.HV', '144.JW', '144.JX', '144.KA', '144.KC', '144.KE', '144.KF', '144.KG'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1225, -1, 2811, -1], 'generators': [40284840, 6227384421, 16, 5167, 1313941668480, 9709928549146, 11536, 7], 'label': '18432.q.72.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.cl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CL', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387300
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.CM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.B', '36.Y'], 'contains': ['144.GT', '144.GU', '144.GW', '144.GY', '144.HQ', '144.HS', '144.HU', '144.HW', '144.JY', '144.JZ', '144.KB', '144.KD', '144.KE', '144.KF', '144.KH'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1165, -1, 3208, -1], 'generators': [40284840, 16, 5606275030426, 5167, 4097506695141, 1313941668480, 11536, 7], 'label': '18432.q.72.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.cm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CM', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387301
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.C', '36.Y'], 'contains': ['144.GZ', '144.HB', '144.HF', '144.HG', '144.JE', '144.JF', '144.JK', '144.JL', '144.JW', '144.JY', '144.KC', '144.KD', '144.KJ', '144.KL', '144.KM'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1276, -1, 2793, -1], 'generators': [16, 7, 11536, 4097506695141, 5167, 4103693803560, 1313941668480, 9709928549146], 'label': '18432.q.72.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.cn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CN', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387302
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.D', '36.Y'], 'contains': ['144.HA', '144.HC', '144.HD', '144.HE', '144.JG', '144.JH', '144.JI', '144.JJ', '144.JX', '144.JZ', '144.KA', '144.KB', '144.KJ', '144.KK', '144.KL'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1184, -1, 2754, -1], 'generators': [5606275030426, 16, 7, 11536, 4097506695141, 5167, 4103693803560, 1313941668480], 'label': '18432.q.72.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.co1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CO', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387303
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.E', '36.BC'], 'contains': ['144.D', '144.E', '144.J', '144.K', '144.O', '144.Q', '144.S', '144.U', '144.X', '144.Z', '144.BA', '144.BC', '144.GI', '144.GK', '144.GM', '144.GO', '144.ID', '144.IG', '144.JM', '144.JO', '144.KG', '144.KI', '144.KO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4026, -1, 4369, -1], 'generators': [6227384421, 127387560, 16, 87102720, 5167, 1313941668480, 11536, 7], 'label': '18432.q.72.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '72.cp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CP', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387304
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.F', '36.BC'], 'contains': ['144.P', '144.R', '144.T', '144.V', '144.Y', '144.Z', '144.BB', '144.BC', '144.IE', '144.IF', '144.JN', '144.JP', '144.KH', '144.KI', '144.KO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4281, -1, 4990, -1], 'generators': [127387560, 16, 87102720, 5167, 4097506695141, 1313941668480, 11536, 7], 'label': '18432.q.72.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '72.cq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CQ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387305
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.G', '36.BB'], 'contains': ['144.GJ', '144.GL', '144.GN', '144.GP', '144.IS', '144.IU', '144.JR', '144.JT', '144.KK', '144.KN', '144.KP'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2559, -1, 621, -1], 'generators': [16703, 5160, 1313941668480, 87107887, 127382407, 16, 4103734078080, 5606321847717], 'label': '18432.q.72.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '72.cr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CR', 'subgroup_fusion': None, 'weyl_group': '96.228'}
  • id: 63387306
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.H', '36.BB'], 'contains': ['144.IT', '144.IV', '144.JS', '144.JU', '144.KM', '144.KN', '144.KP'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2617, -1, 802, -1], 'generators': [16703, 5160, 1313941668480, 87107887, 127382407, 16, 4103734078080, 5606321841949], 'label': '18432.q.72.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '72.cs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CS', 'subgroup_fusion': None, 'weyl_group': '96.228'}
  • id: 63387307
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Y'], 'contains': ['144.GS', '144.GU', '144.GX', '144.GY', '144.HA', '144.HC', '144.HF', '144.HG', '144.KT', '144.KV', '144.KW', '144.KY', '144.KZ', '144.LD', '144.LF'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1850, -1, 3243, -1], 'generators': [23, 40284840, 4103734078080, 6227384421, 9709928554906, 5167, 1313941668480, 11536], 'label': '18432.q.72.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.ct1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CT', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387308
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.Y'], 'contains': ['144.GR', '144.GT', '144.GV', '144.GW', '144.GZ', '144.HB', '144.HD', '144.HE', '144.KT', '144.KU', '144.KV', '144.LA', '144.LB', '144.LC', '144.LE'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1579, -1, 3435, -1], 'generators': [23, 11536, 1313941668480, 5167, 6227384421, 40284840, 4103734078080, 9709928549146], 'label': '18432.q.72.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.cu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387309
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A'], 'contains': ['32.B', '48.A', '48.B', '48.C', '64.D', '64.E', '64.J', '64.L'], 'core': '18432.a1', 'coset_action_label': '16T1792', 'count': 16, 'diagramx': [4109, -1, 2076, -1], 'generators': [93409310300, 6227384421, 7, 843, 87102720, 16, 127387560, 5167, 11536], 'label': '18432.q.16.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.A', 'old_label': '16.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.A', 'subgroup_fusion': None, 'weyl_group': '1152.157861'}
  • id: 63387310
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.K', '36.L', '36.P'], 'contains': ['144.DO', '144.DQ', '144.DT', '144.EH', '144.EI', '144.EO', '144.LG', '144.LI', '144.LU', '144.LW', '144.LZ'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8923, -1, 8989, -1], 'generators': [18301133924517, 4103734078080, 87102736, 5167, 180591240257, 1313941668480, 11536, 7], 'label': '18432.q.72.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.cv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CV', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387312
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Q', '36.W', '36.Y'], 'contains': ['144.HP', '144.HQ', '144.JH', '144.JL', '144.KZ', '144.LA', '144.LH', '144.LJ', '144.LM'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2295, -1, 3593, -1], 'generators': [4103734078080, 40284856, 5167, 9709928558626, 1313941668480, 11536, 6354044781, 40284847], 'label': '18432.q.72.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.cx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CX', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387313
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.R', '36.W', '36.X'], 'contains': ['144.EK', '144.EL', '144.II', '144.IJ', '144.IM', '144.LH', '144.LL', '144.LN'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6654, -1, 8001, -1], 'generators': [4103734078080, 40284856, 5606321841949, 5167, 1313941668480, 11536, 40284847, 6354044770], 'label': '18432.q.72.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.cy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CY', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387314
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Q', '36.X', '36.Y'], 'contains': ['144.HR', '144.HS', '144.JF', '144.JG', '144.LB', '144.LF', '144.LH', '144.LK', '144.LM'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2240, -1, 3629, -1], 'generators': [4103734078080, 40284856, 5606321851429, 5167, 1313941668480, 11536, 6354044781, 40284847], 'label': '18432.q.72.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.cz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CZ', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387315
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.DA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.K', '36.R', '36.Y'], 'contains': ['144.DE', '144.DS', '144.EM', '144.EN', '144.HT', '144.HU', '144.IH', '144.IK', '144.JE', '144.JI', '144.KR', '144.KY', '144.LC', '144.LH', '144.LI', '144.LY'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7544, -1, 8446, -1], 'generators': [4103734078080, 6227384421, 40284856, 5167, 9709928558626, 1313941668480, 11536, 40284847], 'label': '18432.q.72.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.da1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DA', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387316
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.S', '36.Y', '36.Z'], 'contains': ['144.HV', '144.HW', '144.JJ', '144.JK', '144.LD', '144.LE', '144.LI', '144.LJ', '144.LK'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2259, -1, 3611, -1], 'generators': [4103734078080, 6227384421, 40284856, 5167, 1313941668480, 9709928549146, 11536, 40284847], 'label': '18432.q.72.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.db1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DB', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387317
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.L', '36.R', '36.Z'], 'contains': ['144.EP', '144.EU', '144.IL', '144.LI', '144.LN'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7907, -1, 8600, -1], 'generators': [4103734078080, 6227384421, 40284856, 5606321841949, 5167, 1313941668480, 11536, 40284847], 'label': '18432.q.72.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.dc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DC', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387318
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.K', '36.L', '36.U'], 'contains': ['144.DU', '144.EQ', '144.ER', '144.LI', '144.MA'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [9228, -1, 9362, -1], 'generators': [40284840, 4103734078080, 11219048432047, 6227383801, 5167, 1313941668480, 11536, 7], 'label': '18432.q.72.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DD', 'subgroup_fusion': None, 'weyl_group': '256.16883'}
  • id: 63387319
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Q', '36.W', '36.Z'], 'contains': ['144.DF', '144.LJ', '144.LM', '144.LN'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3072, -1, 4055, -1], 'generators': [4103734078080, 40284856, 5167, 1313941668480, 9709928549146, 11536, 6354044781, 40284847], 'label': '18432.q.72.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.de1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DE', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387320
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.C'], 'contains': ['32.C', '48.F', '48.G', '64.A', '64.C'], 'core': '18432.a1', 'coset_action_label': '16T1796', 'count': 16, 'diagramx': [3102, -1, 238, -1], 'generators': [4103734078080, 6611, 11543, 5606321851418, 87107887, 1313941668480, 93409313763, 127376056, 16687], 'label': '18432.q.16.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '16.b1', 'projective_image': '18432.q', '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': '1152.155467'}
  • id: 63387321
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.M', '36.S', '36.W'], 'contains': ['144.DV', '144.LJ', '144.LL'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7984, -1, 7528, -1], 'generators': [4103734078080, 40284856, 5167, 1313941668480, 9709928549146, 11536, 40284847, 6354044770], 'label': '18432.q.72.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.df1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DF', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387322
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Q', '36.X', '36.Z'], 'contains': ['144.KS', '144.LK', '144.LM', '144.LN'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3047, -1, 4073, -1], 'generators': [4103734078080, 40284856, 5606321841949, 5167, 1313941668480, 11536, 6354044781, 40284847], 'label': '18432.q.72.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.dg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DG', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387323
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.N', '36.S', '36.X'], 'contains': ['144.LK', '144.LL', '144.MB'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [8020, -1, 7559, -1], 'generators': [4103734078080, 40284856, 5606321851429, 5167, 1313941668480, 11536, 40284847, 6354044770], 'label': '18432.q.72.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.dh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DH', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387324
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.M', '36.N', '36.V'], 'contains': ['144.DX', '144.ET', '144.LL', '144.MD'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8797, -1, 8076, -1], 'generators': [40284840, 4103734078080, 5167, 1313941668480, 11536, 11219135523247, 6354045361, 7], 'label': '18432.q.72.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.di1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DI', 'subgroup_fusion': None, 'weyl_group': '256.5695'}
  • id: 63387325
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.DJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.O', '36.P', '36.BA'], 'contains': ['144.CY', '144.DA', '144.DB', '144.DY', '144.DZ', '144.EB', '144.EV', '144.EZ', '144.FC', '144.LG', '144.LO', '144.ME', '144.MF', '144.MH'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6431, -1, 6670, -1], 'generators': [18301133924517, 4103734078080, 127387560, 87102736, 5167, 1313941668480, 11536, 7], 'label': '18432.q.72.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.dj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DJ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387326
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Q', '36.R', '36.BB'], 'contains': ['144.CZ', '144.EW', '144.FD', '144.IN', '144.IO', '144.IQ', '144.IS', '144.IT', '144.KQ', '144.KU', '144.KX', '144.LH', '144.LN', '144.LO'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4179, -1, 4810, -1], 'generators': [4103734078080, 127387576, 87102720, 5606321841949, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.72.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.dk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DK', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387327
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.P', '36.R', '36.S', '36.T', '36.U', '36.V', '36.BC'], 'contains': ['144.EA', '144.EX', '144.FA', '144.FE', '144.FF', '144.ID', '144.IE', '144.IP', '144.LI', '144.LL', '144.LO', '144.MG'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7926, -1, 7679, -1], 'generators': [4103734078080, 6227384421, 127387576, 87102720, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.72.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.dl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DL', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 63387328
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.Q', '36.S', '36.BB'], 'contains': ['144.IR', '144.IU', '144.IV', '144.KW', '144.KX', '144.LJ', '144.LK', '144.LO'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2990, -1, 3577, -1], 'generators': [4103734078080, 127387576, 87102720, 5606321851429, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.72.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.dm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DM', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387329
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.O', '36.T', '36.BA'], 'contains': ['144.DC', '144.DD', '144.EC', '144.EY', '144.LO', '144.MH'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6136, -1, 5870, -1], 'generators': [4103734078080, 127387560, 20835531390117, 87102736, 5167, 1313941668480, 11536, 7], 'label': '18432.q.72.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '72.dn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DN', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387330
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.O', '36.Q', '36.BC'], 'contains': ['144.FB', '144.FG', '144.IF', '144.IG', '144.LM', '144.LO'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [4453, -1, 5243, -1], 'generators': [4103734078080, 6227384410, 127387576, 87102720, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.72.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.do1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DO', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 63387331
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.C', '8.B'], 'contains': ['32.D', '48.BG', '48.BI', '64.C', '64.G'], 'core': '1152.A', 'coset_action_label': None, 'count': 8, 'diagramx': [3159, -1, 1127, -1], 'generators': [4103734078080, 5606321851429, 87102736, 5167, 93409310291, 1313941668480, 11536, 40284847, 843], 'label': '18432.q.16.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '16.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.C', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 63387332
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.DP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.I', '36.Y'], 'contains': ['144.HI', '144.HK', '144.HN', '144.HO', '144.JX', '144.JZ', '144.KC', '144.KD', '144.KY', '144.LA', '144.LE', '144.LF', '144.LP', '144.LR', '144.LS'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1206, -1, 2829, -1], 'generators': [4103734078080, 6227384421, 16, 5167, 1313941668480, 9709928549146, 11536, 7], 'label': '18432.q.72.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.dp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DP', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387333
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.J', '24.K', '36.Y'], 'contains': ['144.HH', '144.HJ', '144.HL', '144.HM', '144.JW', '144.JY', '144.KA', '144.KB', '144.KZ', '144.LB', '144.LC', '144.LD', '144.LP', '144.LQ', '144.LR'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2017, -1, 2614, -1], 'generators': [4103734078080, 6227384421, 16, 5167, 1313941668480, 11536, 8396027160338, 7], 'label': '18432.q.72.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.dq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DQ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387334
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.M', '36.W', '36.Y', '36.BB'], 'contains': ['144.DK', '144.ED', '144.HX', '144.IW', '144.IX', '144.JA', '144.JR', '144.JS', '144.KE', '144.KJ', '144.KU', '144.KW', '144.LH', '144.LJ', '144.LQ', '144.LS', '144.LT'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2581, -1, 2396, -1], 'generators': [4103734078080, 16, 87102720, 5606321841949, 5167, 1313941668480, 11536, 7], 'label': '18432.q.72.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.dr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DR', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387335
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.L', '36.X', '36.Y', '36.BB'], 'contains': ['144.HY', '144.IY', '144.JB', '144.KF', '144.KK', '144.KM', '144.KT', '144.LH', '144.LK', '144.LP', '144.LT'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2277, -1, 2631, -1], 'generators': [87102727, 4103734078080, 127387560, 5606321851429, 87102736, 5167, 1313941668480, 11536], 'label': '18432.q.72.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '72.ds1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DS', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 63387336
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.N', '36.Y', '36.Z', '36.BC'], 'contains': ['144.DG', '144.DJ', '144.DL', '144.HZ', '144.IA', '144.IB', '144.IZ', '144.JM', '144.JN', '144.KG', '144.KH', '144.KL', '144.KV', '144.LI', '144.LM', '144.LR', '144.LT'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2731, -1, 3867, -1], 'generators': [40284840, 4103734078080, 6227384421, 16, 5167, 1313941668480, 11536, 7], 'label': '18432.q.72.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.dt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DT', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387337
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.O', '36.W', '36.Z', '36.BB'], 'contains': ['144.JC', '144.KN', '144.LJ', '144.LN', '144.LT'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2884, -1, 3225, -1], 'generators': [87102727, 4103734078080, 127387560, 87102736, 5606321841949, 5167, 1313941668480, 11536], 'label': '18432.q.72.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '72.du1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DU', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 63387338
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.P', '36.X', '36.Z', '36.BB'], 'contains': ['144.JD', '144.JT', '144.JU', '144.KX', '144.LK', '144.LN', '144.LS', '144.LT'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2832, -1, 2771, -1], 'generators': [4103734078080, 16, 87102720, 5167, 1313941668480, 9709928549146, 11536, 7], 'label': '18432.q.72.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.dv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387339
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.Q', '36.W', '36.X', '36.BC'], 'contains': ['144.DH', '144.DI', '144.IC', '144.JO', '144.JP', '144.KI', '144.LL', '144.LM', '144.LT'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3913, -1, 4423, -1], 'generators': [40284840, 4103734078080, 16, 5167, 1313941668480, 11536, 6354044781, 7], 'label': '18432.q.72.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '72.dw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DW', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387340
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.K'], 'contains': ['144.FH', '144.FI', '144.FL', '144.FM', '144.GF', '144.GG', '144.LW', '144.LY', '144.MA', '144.MI', '144.MJ'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [9251, -1, 9171, -1], 'generators': [87181926493, 4103734078080, 127387560, 5167, 1313941668480, 11536, 8396027160338, 13834520547263], 'label': '18432.q.72.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '72.dx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DX', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387341
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.N'], 'contains': ['144.LX', '144.MB', '144.MD'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8899, -1, 8299, -1], 'generators': [11300079536047, 4103734078080, 5606321847709, 127387560, 87258503650, 5167, 1313941668480, 11536], 'label': '18432.q.72.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.N', 'old_label': '72.dy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DY', 'subgroup_fusion': None, 'weyl_group': '256.4741'}
  • id: 63387342
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.C', '8.B'], 'contains': ['32.D', '48.BH', '48.BJ', '64.A', '64.B', '64.G'], 'core': '1152.A', 'coset_action_label': None, 'count': 8, 'diagramx': [3128, -1, 591, -1], 'generators': [4103734078080, 16, 93409310300, 5167, 1313941668480, 11536, 8396027160338, 843, 7], 'label': '18432.q.16.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '16.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.D', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 63387343
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.K'], 'contains': ['144.FJ', '144.FK', '144.FN', '144.FO', '144.LY', '144.LZ', '144.MA'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [9301, -1, 9321, -1], 'generators': [4103734078080, 87181926490, 127387560, 5167, 1313941668480, 11536, 8396027160338, 11300123081647], 'label': '18432.q.72.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '72.dz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DZ', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387344
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.N'], 'contains': ['144.MB', '144.MC', '144.MD'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8870, -1, 8332, -1], 'generators': [4103734078080, 5606321847709, 13834477001663, 127387560, 87258503653, 5167, 1313941668480, 11536], 'label': '18432.q.72.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.N', 'old_label': '72.ea1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EA', 'subgroup_fusion': None, 'weyl_group': '256.4741'}
  • id: 63387345
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['36.P'], 'contains': ['144.FP', '144.FQ', '144.FU', '144.FW', '144.FX', '144.FZ', '144.GD', '144.GE', '144.LU', '144.LV', '144.LZ', '144.MC', '144.ME', '144.MG', '144.MH'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8536, -1, 8056, -1], 'generators': [4103734078080, 40284856, 16906281265317, 5167, 180591240257, 1313941668480, 11536, 127387567], 'label': '18432.q.72.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '72.eb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EB', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387346
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.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': ['24.T', '36.P'], 'contains': ['144.FR', '144.FS', '144.FT', '144.FV', '144.FY', '144.GA', '144.GB', '144.GC', '144.LU', '144.LV', '144.LW', '144.LX', '144.ME', '144.MF', '144.MG'], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8233, -1, 7965, -1], 'generators': [4103734078080, 180591240262, 40284856, 16906281265317, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.72.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '72.ec1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EC', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387347
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.ED', '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': ['36.B'], 'contains': ['144.MK', '144.ML', '144.MO', '144.MP', '144.MV', '144.MX', '144.NA', '144.NB', '144.NW', '144.NY', '144.OA', '144.OH', '144.OJ', '144.ON', '144.OO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7148, -1, 6894, -1], 'generators': [127387560, 180591223822, 5183, 16906314287397, 87091216, 7, 2789792414767, 1313941680016], 'label': '18432.q.72.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '72.ed1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ED', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387348
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.EE', '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': ['36.B'], 'contains': ['144.MK', '144.ML', '144.MM', '144.MN', '144.MU', '144.MW', '144.MY', '144.MZ', '144.NW', '144.NX', '144.NY', '144.OI', '144.OK', '144.OL', '144.OM'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7227, -1, 6795, -1], 'generators': [127387560, 2789792414767, 7, 87091216, 5183, 180591223822, 1313941680016, 18301210492197], 'label': '18432.q.72.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '72.ee1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EE', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387349
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.EF', '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': ['36.B'], 'contains': ['144.MU', '144.MW', '144.NA', '144.NB', '144.NE', '144.NF', '144.NI', '144.NJ', '144.OH', '144.OI', '144.OM', '144.OO', '144.OQ', '144.OS', '144.OT'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7061, -1, 6876, -1], 'generators': [127387560, 87102720, 180591240241, 11520, 19440635185317, 5160, 2789792414767, 1313941680016], 'label': '18432.q.72.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '72.ef1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387350
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '72.EG', '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': ['24.U', '36.B'], 'contains': ['144.MV', '144.MX', '144.MY', '144.MZ', '144.NE', '144.NF', '144.NG', '144.NH', '144.OJ', '144.OK', '144.OL', '144.ON', '144.OQ', '144.OR', '144.OS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6635, -1, 6644, -1], 'generators': [127387560, 2789792414767, 7, 180591223822, 87096383, 16, 1313941680016, 16906314287397], 'label': '18432.q.72.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '72.eg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EG', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387351
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.E', '48.A'], 'contains': ['192.B', '192.I', '192.J', '192.CY', '192.DH'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3740, -1, 2122, -1], 'generators': [6227384421, 5160, 11520, 87102720, 127387560, 6611, 1313941668480], 'label': '18432.q.96.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '96.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.A', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387352
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.F', '48.A'], 'contains': ['192.B', '192.K', '192.L'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3624, -1, 2069, -1], 'generators': [6611, 5160, 11520, 4097506695141, 87102720, 127387560, 1313941668480], 'label': '18432.q.96.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '96.b1', 'projective_image': '18432.q', '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': '96.226'}
  • id: 63387353
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.A', '8.B'], 'contains': ['32.D', '48.BK', '48.BL', '48.BM', '64.D', '64.E', '64.H'], 'core': '1152.A', 'coset_action_label': None, 'count': 8, 'diagramx': [3868, -1, 1701, -1], 'generators': [4103734078080, 6227384421, 16, 93409310300, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.16.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '16.e1', 'projective_image': '18432.q', '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': None}
  • id: 63387354
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.E', '48.A'], 'contains': ['192.C', '192.I', '192.K', '192.CX', '192.DD'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3664, -1, 2157, -1], 'generators': [127370903, 6227384421, 16, 1313941668480, 87091216, 843, 7], 'label': '18432.q.96.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '96.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.C', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387355
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.F', '48.A'], 'contains': ['192.C', '192.J', '192.L'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3640, -1, 2084, -1], 'generators': [127370903, 16, 4097506695141, 1313941668480, 87091216, 843, 7], 'label': '18432.q.96.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '96.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.D', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387356
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.N', '48.A'], 'contains': ['192.A', '192.I', '192.L', '192.S', '192.BG'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3369, -1, 1999, -1], 'generators': [40284840, 5160, 1313941668480, 11520, 6611, 6227384421, 4103734078080], 'label': '18432.q.96.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '96.e1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.E', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387357
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.Q', '48.A'], 'contains': ['192.J', '192.K', '192.S'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3592, -1, 2099, -1], 'generators': [40284840, 4103734078080, 6611, 11520, 1313941668480, 5160, 6354044781], 'label': '18432.q.96.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '96.f1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.F', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387358
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5275, -1, 4455, -1], 'generators': [87102720, 93409309459, 2789792409607, 1313941668496, 5167, 11536, 1313988496680], 'label': '18432.q.96.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.G', 'old_label': '96.g1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.G', 'subgroup_fusion': None, 'weyl_group': '192.1541'}
  • id: 63387359
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.M', '48.G'], 'contains': ['192.D', '192.G', '192.U', '192.V', '192.W'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [875, -1, 324, -1], 'generators': [4103734078080, 6611, 11543, 5606321851418, 87107887, 1313941668480, 16687], 'label': '18432.q.96.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.G', 'old_label': '96.h1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.H', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387360
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.P', '48.G'], 'contains': ['192.V', '192.W'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [969, -1, 983, -1], 'generators': [4103734078080, 6611, 11543, 87107887, 1313941668480, 9709928549146, 16687], 'label': '18432.q.96.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.G', 'old_label': '96.i1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.I', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387361
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.J', '32.A'], 'contains': ['192.O', '192.P', '192.Q', '192.R', '192.X', '192.Z', '192.BB'], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [2469, -1, 965, -1], 'generators': [4103734078080, 6227384402, 40279680, 1313941668480, 5606321841938, 87091200, 843], 'label': '18432.q.96.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.J', 'old_label': '96.j1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.J', 'subgroup_fusion': None, 'weyl_group': '96.144'}
  • id: 63387362
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['32.A', '48.M'], 'contains': ['192.Y', '192.BA', '192.BC'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [908, -1, 259, -1], 'generators': [6920176419218, 6227384421, 16, 5167, 11536, 843, 7], 'label': '18432.q.96.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.M', 'old_label': '96.k1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.K', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387363
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.B', '48.E', '48.S'], 'contains': ['192.BC', '192.BE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3171, -1, 1791, -1], 'generators': [40284840, 6227384421, 16, 5167, 11536, 843, 7], 'label': '18432.q.96.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.E', 'old_label': '96.l1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.L', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 63387364
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['32.E', '32.F', '32.G', '144.MI', '256.F'], 'core': '1152.A', 'coset_action_label': None, 'count': 16, 'diagramx': [4758, -1, 4645, -1], 'generators': [4103734078080, 11219048432047, 6227384402, 5167, 93409310291, 1313941668480, 11536, 8396027160338, 843], 'label': '18432.q.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': '18432.q', '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': '1152.157849'}
  • id: 63387365
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.B', '48.E', '48.U'], 'contains': ['192.BE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3562, -1, 1910, -1], 'generators': [40284840, 16, 5167, 11536, 6354044781, 843, 7], 'label': '18432.q.96.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.E', 'old_label': '96.m1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.M', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 63387366
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.R', '32.B', '48.A'], 'contains': ['192.B', '192.C', '192.E', '192.S'], 'core': '18432.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3708, -1, 2035, -1], 'generators': [4103734078080, 127387560, 87102720, 11520, 1313941668480, 5160, 843], 'label': '18432.q.96.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.A', 'old_label': '96.n1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.N', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 63387368
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.S', '32.B', '48.C'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4330, -1, 3898, -1], 'generators': [4103606723880, 16, 93409309459, 2789705329920, 5167, 11536, 7], 'label': '18432.q.96.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.A', 'old_label': '96.p1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.P', 'subgroup_fusion': None, 'weyl_group': '1152.157861'}
  • id: 63387369
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.D', '48.F', '48.V'], 'contains': ['192.Y', '192.BF'], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1003, -1, 191, -1], 'generators': [4103734078080, 174363845176, 87096376, 1313941668480, 5606321841938, 87091200, 127376056], 'label': '18432.q.96.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.G', 'old_label': '96.q1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.Q', 'subgroup_fusion': None, 'weyl_group': '192.1000'}
  • id: 63387370
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.D', '48.F', '48.Z'], 'contains': ['192.BF'], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1031, -1, 136, -1], 'generators': [4103734078080, 174363845176, 87096376, 5606321851418, 1313941668480, 87091200, 127376056], 'label': '18432.q.96.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.G', 'old_label': '96.r1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.R', 'subgroup_fusion': None, 'weyl_group': '192.1000'}
  • id: 63387371
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.D', '48.BA', '48.BB'], 'contains': ['192.BE', '192.BF'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2362, -1, 1010, -1], 'generators': [127387560, 16, 5167, 1314028771200, 11536, 843, 7], 'label': '18432.q.96.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '96.s1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.S', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63387372
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.E', '48.BA', '48.BB'], 'contains': ['192.BE', '192.BF'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2713, -1, 1604, -1], 'generators': [127387560, 16, 5167, 11536, 4103646998400, 843, 7], 'label': '18432.q.96.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '96.t1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.T', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387373
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.R', '32.C', '48.G'], 'contains': ['192.F', '192.H', '192.W'], 'core': '18432.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3103, -1, 1293, -1], 'generators': [4103734078080, 11543, 87107887, 1313941668480, 127376056, 843, 16687], 'label': '18432.q.96.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '96.u1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.U', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 63387374
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['32.C', '48.F', '48.BB'], 'contains': ['192.BF'], 'core': '18432.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1656, -1, 416, -1], 'generators': [16, 5167, 11536, 4103646998400, 1313988496680, 843, 7], 'label': '18432.q.96.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '96.v1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.V', 'subgroup_fusion': None, 'weyl_group': '288.411'}
  • id: 63387375
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '18.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1'], 'contains': ['36.F', '36.G', '36.I', '36.J', '36.K', '36.L', '36.P', '36.R', '36.U'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [9227, -1, 9360, -1], 'generators': [87181926493, 23, 4103734078080, 127387560, 87102720, 5606321841949, 5167, 1313941668480, 11536, 11300123081647], 'label': '18432.q.18.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.A', 'subgroup_fusion': None, 'weyl_group': '2880.ec'}
  • id: 63387376
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '32.C'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4750, -1, 2200, -1], 'generators': [16, 2789745614760, 93409309459, 5167, 1314028771200, 11536, 7], 'label': '18432.q.96.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.C', 'old_label': '96.w1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.W', 'subgroup_fusion': None, 'weyl_group': '576.8663'}
  • id: 63387377
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.S', '48.H'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4799, -1, 4200, -1], 'generators': [4103606723880, 1314028771200, 5167, 1313941668496, 2789792409607, 93409309459, 11536], 'label': '18432.q.96.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.H', 'old_label': '96.x1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.X', 'subgroup_fusion': None, 'weyl_group': '384.20164'}
  • id: 63387378
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.E', '48.BK'], 'contains': ['192.N', '192.BH', '192.BL', '192.BV', '192.BX'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3450, -1, 1854, -1], 'generators': [6227384421, 87102736, 5167, 1313941668480, 860, 11536, 40284847], 'label': '18432.q.96.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BK', 'old_label': '96.y1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.Y', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387379
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.F', '48.BK'], 'contains': ['192.BL', '192.BW', '192.BX'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3421, -1, 1811, -1], 'generators': [87102736, 5167, 4097506695141, 1313941668480, 860, 11536, 40284847], 'label': '18432.q.96.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BK', 'old_label': '96.z1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.Z', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387380
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.C', '48.BE'], 'contains': ['192.BM', '192.BO', '192.BP', '192.CA', '192.CB', '192.CE', '192.CF'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [83, -1, 1332, -1], 'generators': [4103693803567, 6920176419218, 5167, 4097506695122, 1313941668480, 11536, 843], 'label': '18432.q.96.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '96.ba1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BA', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387381
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.D', '48.BE'], 'contains': ['192.BM', '192.BN', '192.BO', '192.BY', '192.BZ', '192.CC', '192.CD'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [114, -1, 1219, -1], 'generators': [4103693803567, 5167, 4097506695122, 1313941668480, 11536, 8396027160338, 843], 'label': '18432.q.96.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '96.bb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BB', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387382
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.G', '48.BH'], 'contains': ['192.M', '192.T', '192.BN', '192.BQ', '192.BR'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1795, -1, 114, -1], 'generators': [174363851543, 16703, 4103734078080, 16, 1313941668480, 5160, 8396027160338], 'label': '18432.q.96.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BH', 'old_label': '96.bc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BC', 'subgroup_fusion': None, 'weyl_group': '96.228'}
  • id: 63387383
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.H', '48.BH'], 'contains': ['192.BP', '192.BQ', '192.BR'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1052, -1, 291, -1], 'generators': [8396027166106, 16703, 5160, 1313941668480, 16, 4103734078080, 174363851543], 'label': '18432.q.96.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BH', 'old_label': '96.bd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BD', 'subgroup_fusion': None, 'weyl_group': '96.228'}
  • id: 63387384
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.I', '48.J', '48.M', '48.N', '48.Q', '48.V', '48.BG'], 'contains': ['192.Y', '192.BS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [510, -1, 925, -1], 'generators': [16703, 4103734078080, 5606321857197, 40279680, 174363856703, 1313941668480, 87107903], 'label': '18432.q.96.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '96.be1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BE', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387385
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.K', '48.L', '48.M', '48.N', '48.R', '48.W', '48.BJ'], 'contains': ['192.BA', '192.BS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [303, -1, 893, -1], 'generators': [16, 5167, 1313941668480, 11536, 8396027160338, 843, 7], 'label': '18432.q.96.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '96.bf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BF', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387386
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.A', '4.C', '6.B', '8.B'], 'core': '2.B', 'coset_action_label': None, 'count': 1, 'diagramx': [3170, 5186, 1542, 5382], 'generators': [11536, 16, 5606321841949, 843, 127387560, 4103734078080, 5167, 7, 1313941668480, 87102720, 93409310300, 6227384421], 'label': '18432.q.2.B', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 63387387
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '18.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': ['9.a1'], 'contains': ['36.M', '36.N', '36.P', '36.S', '36.V'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7877, -1, 7877, -1], 'generators': [87181926493, 11536, 1313941668480, 11300046513967, 5167, 87102720, 127387560, 23, 4103734078080, 5606321851429], 'label': '18432.q.18.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.B', 'subgroup_fusion': None, 'weyl_group': '2880.eh'}
  • id: 63387388
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.I', '48.K', '48.M', '48.O', '48.S', '48.X', '48.BL'], 'contains': ['192.BC', '192.BS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1458, -1, 1368, -1], 'generators': [6227384421, 16, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.96.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '96.bg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BG', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387389
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.K', '48.L', '48.O', '48.P', '48.Q', '48.Y', '48.BG'], 'contains': ['192.BS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [243, -1, 1068, -1], 'generators': [16703, 4103734078080, 5606321851429, 40279680, 174363856703, 1313941668480, 87107903], 'label': '18432.q.96.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '96.bh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BH', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387390
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.J', '48.L', '48.N', '48.P', '48.T', '48.X', '48.BL'], 'contains': ['192.BS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [262, -1, 1139, -1], 'generators': [16, 5167, 4097506695141, 1313941668480, 11536, 843, 7], 'label': '18432.q.96.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '96.bi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BI', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387391
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.I', '48.J', '48.O', '48.P', '48.R', '48.W', '48.BN'], 'contains': ['192.BS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [188, -1, 1050, -1], 'generators': [16, 5606321841949, 5167, 2789792409600, 11536, 843, 7], 'label': '18432.q.96.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '96.bj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BJ', 'subgroup_fusion': None, 'weyl_group': '384.17948'}
  • id: 63387392
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.Q', '48.R', '48.S', '48.T', '48.U', '48.BA', '48.BO'], 'contains': ['192.BE', '192.BS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1933, -1, 1638, -1], 'generators': [16, 87102720, 5167, 2789792409600, 11536, 843, 7], 'label': '18432.q.96.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.bk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BK', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387393
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.BA', '48.BB', '48.BO'], 'contains': ['192.BE', '192.BF', '192.BS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1081, -1, 1174, -1], 'generators': [16, 87102720, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.96.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.R', 'old_label': '96.bl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BL', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 63387394
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['48.V', '48.W', '48.X', '48.Y', '48.Z', '48.BB', '48.BO'], 'contains': ['192.BF', '192.BS'], 'core': '18432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [589, -1, 720, -1], 'generators': [16, 5167, 2789792409600, 11536, 4103646998400, 843, 7], 'label': '18432.q.96.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '96.bm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BM', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387395
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.A', '48.BE'], 'contains': ['192.BT', '192.BU', '192.BV', '192.BY', '192.CA', '192.CC', '192.CE'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [150, -1, 1455, -1], 'generators': [6227384402, 5167, 1313941668480, 11536, 8396027160338, 40284847, 843], 'label': '18432.q.96.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '96.bn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BN', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 63387396
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.B', '48.BE'], 'contains': ['192.BT', '192.BU', '192.BW', '192.BZ', '192.CB', '192.CD', '192.CF'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [61, -1, 1393, -1], 'generators': [6920176419218, 5167, 4097506695122, 1313941668480, 11536, 40284847, 843], 'label': '18432.q.96.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '96.bo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BO', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 63387397
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.L', '48.BC', '48.BE', '48.BH'], 'contains': ['192.BN', '192.BP', '192.BT', '192.CG', '192.CJ'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [394, -1, 1264, -1], 'generators': [23, 4103734078080, 5167, 174440412856, 1313941668480, 11536, 8396027160338], 'label': '18432.q.96.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '96.bp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BP', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 63387398
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '18.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': ['9.a1'], 'contains': ['36.H', '36.R', '36.T', '36.V'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7242, -1, 7928, -1], 'generators': [87181926493, 11536, 1313941668480, 11300046513967, 5167, 87102720, 127387560, 23, 4103734078080, 5606321841949], 'label': '18432.q.18.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.C', 'subgroup_fusion': None, 'weyl_group': '2400.ec'}
  • id: 63387399
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.M', '48.BD', '48.BE', '48.BI'], 'contains': ['192.BM', '192.BU', '192.CG', '192.CK', '192.CN'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [431, -1, 1430, -1], 'generators': [4103734078080, 87102736, 5167, 1313941668480, 11536, 8396027160338, 843], 'label': '18432.q.96.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '96.bq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BQ', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 63387400
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.N', '48.BE', '48.BF', '48.BK'], 'contains': ['192.BO', '192.BV', '192.BW', '192.CG', '192.CL'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [463, -1, 1570, -1], 'generators': [4103734078080, 6227384421, 5167, 1313941668480, 11536, 851, 40284847], 'label': '18432.q.96.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '96.br1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BR', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 63387401
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.O', '48.BD', '48.BF', '48.BH'], 'contains': ['192.BQ', '192.CG'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [948, -1, 1116, -1], 'generators': [23, 4103734078080, 5167, 174440412856, 1313941668480, 11536, 8396027169818], 'label': '18432.q.96.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '96.bs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BS', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 63387402
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.P', '48.BC', '48.BF', '48.BI'], 'contains': ['192.CG', '192.CN'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [618, -1, 1542, -1], 'generators': [4103734078080, 87102736, 5167, 1313941668480, 11536, 6920223230757, 851], 'label': '18432.q.96.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '96.bt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BT', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 63387403
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.Q', '48.BC', '48.BD', '48.BK'], 'contains': ['192.BX', '192.CG'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2180, -1, 1659, -1], 'generators': [4103734078080, 5167, 1313941668480, 11536, 6314485093, 40284847, 843], 'label': '18432.q.96.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '96.bu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BU', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 63387404
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.R', '32.D', '48.BH', '48.BI', '48.BK'], 'contains': ['192.BL', '192.BR', '192.CG'], 'core': '1152.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2778, -1, 1519, -1], 'generators': [4103734078080, 87102736, 5167, 1313941668480, 11536, 40284847, 843], 'label': '18432.q.96.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '96.bv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BV', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 63387405
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['32.D', '48.BG', '48.BJ', '48.BL', '48.BN', '48.BO'], 'contains': ['192.BS'], 'core': '1152.A', 'coset_action_label': None, 'count': 2, 'diagramx': [358, -1, 1089, -1], 'generators': [4103734078080, 16, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.96.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '96.bw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BW', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
  • id: 63387406
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '32.D', '48.BM'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 16, 'diagramx': [4125, -1, 2244, -1], 'generators': [4103734078080, 16, 93409309459, 5167, 1313941668480, 11536, 7], 'label': '18432.q.96.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.E', 'old_label': '96.bx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BX', 'subgroup_fusion': None, 'weyl_group': '1152.157861'}
  • id: 63387407
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '48.BP', '48.BQ', '48.BR'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5048, -1, 4884, -1], 'generators': [4103734078080, 127387576, 87102720, 93409309459, 5167, 1313941668480, 11536], 'label': '18432.q.96.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.T', 'old_label': '96.by1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BY', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 63387408
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.T', '32.E'], 'contains': ['192.CH', '192.CI', '192.CM'], 'core': '1152.A', 'coset_action_label': None, 'count': 96, 'diagramx': [5019, -1, 4698, -1], 'generators': [4103734078080, 6227384421, 93409309459, 19615115146917, 5167, 1313941668480, 11536], 'label': '18432.q.96.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BZ', 'old_label': '96.bz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.BZ', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387409
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '18.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': ['9.a1'], 'contains': ['36.S', '36.T', '36.U'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7273, -1, 7415, -1], 'generators': [87181926493, 23, 4103734078080, 127387560, 87102720, 5606321851429, 5167, 1313941668480, 11536, 11300123081647], 'label': '18432.q.18.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.D', 'subgroup_fusion': None, 'weyl_group': '8640.t'}
  • id: 63387410
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.I', '48.BE'], 'contains': ['192.BY', '192.BZ', '192.CE', '192.CF', '192.CJ', '192.CL', '192.CN'], 'core': '1152.A', 'coset_action_label': None, 'count': 48, 'diagramx': [25, -1, 1476, -1], 'generators': [4103734078080, 9709928554906, 6266944090, 5167, 1313941668480, 11536, 843], 'label': '18432.q.96.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '96.ca1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CA', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 63387411
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.K', '32.F', '48.BE'], 'contains': ['192.CA', '192.CB', '192.CC', '192.CD', '192.CJ', '192.CK', '192.CL'], 'core': '1152.A', 'coset_action_label': None, 'count': 48, 'diagramx': [215, -1, 1313, -1], 'generators': [4103734078080, 6266944090, 5167, 1313941668480, 11536, 8396027160338, 843], 'label': '18432.q.96.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '96.cb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CB', 'subgroup_fusion': None, 'weyl_group': '192.1537'}
  • id: 63387412
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.S'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [5199, -1, 4439, -1], 'generators': [16, 2789792414767, 7, 127376056, 93409309459, 87102720, 1313941680016], 'label': '18432.q.96.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CC', 'old_label': '96.cc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CC', 'subgroup_fusion': None, 'weyl_group': '192.1541'}
  • id: 63387413
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '48.BS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5297, -1, 4491, -1], 'generators': [127387560, 93409309459, 11543, 87091216, 16687, 2789792414767, 1313941680016], 'label': '18432.q.96.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BS', 'old_label': '96.cd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CD', 'subgroup_fusion': None, 'weyl_group': '384.18221'}
  • id: 63387414
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '48.BT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6152, -1, 4660, -1], 'generators': [127370903, 16696, 87102720, 93409309459, 5183, 2789792414767, 1313941680016], 'label': '18432.q.96.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BT', 'old_label': '96.cd2', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CE', 'subgroup_fusion': None, 'weyl_group': '384.20164'}
  • id: 63387415
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.S', '48.BU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4849, -1, 4406, -1], 'generators': [127370903, 16, 93409309459, 87091216, 7, 2789792414767, 1313941680016], 'label': '18432.q.96.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BU', 'old_label': '96.ce1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CF', 'subgroup_fusion': None, 'weyl_group': '384.20164'}
  • id: 63387416
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.S', '48.BV', '48.BW', '48.BX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5216, -1, 4628, -1], 'generators': [127387560, 2789792414767, 7, 93409309459, 87096383, 16, 1313941680016], 'label': '18432.q.96.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.U', 'old_label': '96.cf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CG', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 63387417
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.T'], 'contains': ['192.CP', '192.CQ', '192.CR'], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4987, -1, 5571, -1], 'generators': [6227384421, 2789792421136, 4103734083247, 19615115146917, 93409305135, 87091216, 127370887], 'label': '18432.q.96.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CH', 'old_label': '96.cg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CH', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387418
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.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': ['24.T', '24.U'], 'contains': ['192.CT', '192.CU', '192.CV'], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5086, -1, 4720, -1], 'generators': [6227384421, 2789792421136, 87102720, 4103734083247, 19615115146917, 93409305135, 127376040], 'label': '18432.q.96.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CI', 'old_label': '96.ch1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CI', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387419
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.CJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.U', '32.I'], 'contains': ['192.DF', '192.DG', '192.DI'], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [5724, -1, 4513, -1], 'generators': [2789705318416, 16, 1307714300762, 2615428580524, 19615115146917, 4103606707223, 7], 'label': '18432.q.96.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CJ', 'old_label': '96.ci1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CJ', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387420
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '18.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.A', '9.a1'], 'contains': ['36.A', '36.B', '36.C', '36.O', '36.P', '36.T', '36.BA', '36.BC'], 'core': '72.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7185, -1, 6909, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 20835531390117, 180591240241, 5167, 1313941668480, 11536, 7], 'label': '18432.q.18.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.e1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.E', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387421
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '96.CK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.U'], 'contains': ['192.DM', '192.DN', '192.DO'], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [5131, -1, 4773, -1], 'generators': [2789792421120, 2789705318416, 1313988491527, 1307714300762, 2615428580524, 19615115146917, 4103734083240], 'label': '18432.q.96.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CK', 'old_label': '96.cj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.CK', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387422
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.C', '32.D', '64.A'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3396, -1, 21, -1], 'generators': [4103734078080, 11543, 1313941668480, 93409319531, 843, 16687], 'label': '18432.q.128.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.A', 'old_label': '128.a1', 'projective_image': '18432.q', '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': '288.1024'}
  • id: 63387423
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.B', '32.C', '32.D', '64.B', '64.C', '64.D'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3513, -1, 206, -1], 'generators': [16, 93409310300, 5167, 11536, 843, 7], 'label': '18432.q.128.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.A', 'old_label': '128.b1', 'projective_image': '18432.q', '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': '192.955'}
  • id: 63387424
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.B', '32.D', '64.E'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [3934, -1, 1957, -1], 'generators': [4103734078080, 11520, 1313941668480, 93409313763, 5160, 843], 'label': '18432.q.128.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.E', 'old_label': '128.c1', 'projective_image': '18432.q', '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': '288.1026'}
  • id: 63387425
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.A', '32.F'], 'contains': ['256.A', '256.B', '256.C'], 'core': '18432.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [3840, -1, 586, -1], 'generators': [6266944090, 5167, 11536, 93485161460, 9709968828818, 843], 'label': '18432.q.128.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.D', 'old_label': '128.d1', 'projective_image': '18432.q', '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': '144.183'}
  • id: 63387426
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '128.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.D', '64.F', '64.G', '64.H'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 16, 'diagramx': [4116, -1, 1751, -1], 'generators': [4103734078080, 5167, 1313941668480, 11536, 93485161460, 843], 'label': '18432.q.128.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '128.e1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.E', 'subgroup_fusion': None, 'weyl_group': '1152.157849'}
  • id: 63387427
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '128.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.B', '32.C'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [3765, -1, 1946, -1], 'generators': [11543, 87107887, 127376056, 93409319531, 843, 16687], 'label': '18432.q.128.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.F', 'old_label': '128.f1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.F', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63387428
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '128.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.C', '64.I'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [4330, -1, 3485, -1], 'generators': [16696, 93409310300, 1314028764863, 5183, 2789745609607, 843], 'label': '18432.q.128.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.I', 'old_label': '128.g1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.G', 'subgroup_fusion': None, 'weyl_group': '288.1025'}
  • id: 63387429
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '128.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.B', '64.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4127, -1, 2716, -1], 'generators': [127370903, 93409304532, 16, 87091216, 843, 7], 'label': '18432.q.128.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.H', 'old_label': '128.h1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.H', 'subgroup_fusion': None, 'weyl_group': '576.8652'}
  • id: 63387430
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '128.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.B', '64.K', '64.L'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5261, -1, 4013, -1], 'generators': [127387560, 87102720, 11520, 93409313763, 5160, 843], 'label': '18432.q.128.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.I', 'old_label': '128.i1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.I', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
  • id: 63387431
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '18.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', '9.a1'], 'contains': ['36.Q', '36.R', '36.S', '36.W', '36.X', '36.Y', '36.Z', '36.BB', '36.BC'], 'core': '72.A', 'coset_action_label': None, 'count': 9, 'diagramx': [3089, -1, 4055, -1], 'generators': [4103734078080, 6227384421, 127387560, 16, 87102720, 5606321841949, 5167, 1313941668480, 11536, 7], 'label': '18432.q.18.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.f1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.F', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387432
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3186, -1, 668, -1], 'generators': [127387560, 16, 87102720, 5606321841949, 1313941668480, 5160, 4103734094783], 'label': '18432.q.144.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CJ', 'old_label': '144.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.A', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387434
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CH'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4687, -1, 5459, -1], 'generators': [6227384421, 1313941673647, 87091216, 4103734078087, 4103606712376, 4103734089600, 1313941680016], 'label': '18432.q.144.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CH', 'old_label': '144.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.C', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387435
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3971, -1, 4219, -1], 'generators': [6227384421, 127387560, 87102720, 11543, 11520, 1313941673647, 1313941680016], 'label': '18432.q.144.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CP', 'old_label': '144.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.D', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387436
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3996, -1, 4243, -1], 'generators': [6227384421, 1313941673647, 7, 87091216, 16, 127387560, 1313941680016], 'label': '18432.q.144.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CP', 'old_label': '144.e1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.E', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387437
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3025, -1, 488, -1], 'generators': [5606321851418, 127370903, 4103734094783, 87107887, 5183, 16696, 1313941668480], 'label': '18432.q.144.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CJ', 'old_label': '144.f1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.F', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387438
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3076, -1, 621, -1], 'generators': [127387560, 16696, 5606321851418, 5183, 1313941668480, 4103734094783, 87091216], 'label': '18432.q.144.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CJ', 'old_label': '144.f2', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.G', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387439
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3051, -1, 545, -1], 'generators': [127387560, 16, 87096383, 5606321841949, 1313941668480, 5160, 4103734094783], 'label': '18432.q.144.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CJ', 'old_label': '144.f3', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.H', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387440
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CH'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4737, -1, 5549, -1], 'generators': [4103606723880, 6227384421, 4103734089623, 87091216, 4103734078096, 1313941673647, 1313941680016], 'label': '18432.q.144.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CH', 'old_label': '144.g1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.I', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387441
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4071, -1, 4313, -1], 'generators': [6227384421, 1313941673647, 7, 127376056, 87102720, 16, 1313941680016], 'label': '18432.q.144.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CP', 'old_label': '144.h1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.J', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387442
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '18.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', '9.a1'], 'contains': ['36.D', '36.E', '36.U', '36.V', '36.BC'], 'core': '72.A', 'coset_action_label': None, 'count': 9, 'diagramx': [6130, -1, 7438, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 5167, 1313941668480, 11536, 6227383817, 11219135523247, 7], 'label': '18432.q.18.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.g1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.G', 'subgroup_fusion': None, 'weyl_group': '512.51574'}
  • id: 63387443
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4095, -1, 4337, -1], 'generators': [6227384421, 11543, 11520, 127376056, 87091216, 1313941673647, 1313941680016], 'label': '18432.q.144.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CP', 'old_label': '144.h2', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.K', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387444
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3161, -1, 644, -1], 'generators': [5606321851418, 127387560, 4103734094783, 87107887, 5183, 16696, 1313941668480], 'label': '18432.q.144.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CJ', 'old_label': '144.i1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.L', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387445
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Z'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5869, -1, 5615, -1], 'generators': [4103606712376, 87091216, 4103734078087, 11520, 5167, 2789792409600, 20835531393818], 'label': '18432.q.144.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.Z', 'old_label': '144.j1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.M', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387446
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.N'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [6140, -1, 6090, -1], 'generators': [4103734089623, 87091216, 4103606712376, 4103734089600, 5167, 2789792409600, 20835531393818], 'label': '18432.q.144.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.N', 'old_label': '144.k1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.N', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387447
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.O', '72.CH', '72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4656, -1, 5287, -1], 'generators': [16703, 6227384421, 16, 87102720, 1313941668480, 127376056, 7], 'label': '18432.q.144.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.l1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.O', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387448
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.O', '72.CI', '72.CQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4434, -1, 5209, -1], 'generators': [16703, 16, 87102720, 4097506704610, 1313941668480, 127376056, 7], 'label': '18432.q.144.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.m1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.P', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387449
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Q', '72.CI', '72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4500, -1, 5070, -1], 'generators': [16703, 6227393890, 16, 87102720, 1313941668480, 127376056, 7], 'label': '18432.q.144.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.n1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.Q', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387450
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Q', '72.CH', '72.CQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4758, -1, 5392, -1], 'generators': [16703, 16, 87102720, 4097506695141, 1313941668480, 127376056, 7], 'label': '18432.q.144.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.o1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.R', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387451
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.R', '72.CH', '72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4776, -1, 5314, -1], 'generators': [4103606723880, 16703, 6227384421, 1313941668480, 4103734078087, 87091216, 4103734078096], 'label': '18432.q.144.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.p1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.S', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387452
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.R', '72.CI', '72.CQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4469, -1, 5226, -1], 'generators': [4103606723880, 16703, 4097506704610, 1313941668480, 4103734078087, 87091216, 4103734078096], 'label': '18432.q.144.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.q1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.T', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387453
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '24.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.C'], 'contains': ['48.I', '48.K', '48.M', '48.O', '48.Q', '48.R', '48.S', '72.CL', '96.BN'], 'core': '18432.a1', 'coset_action_label': '24T12426', 'count': 12, 'diagramx': [505, -1, 1497, -1], 'generators': [40284840, 6227384421, 16, 5167, 1313941668480, 9709928549146, 11536, 843, 7], 'label': '18432.q.24.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '24.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.A', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387454
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.S', '72.CI', '72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4369, -1, 5027, -1], 'generators': [4103606723880, 4103734078096, 87091216, 4103734078087, 4097506695141, 16703, 1313941668480], 'label': '18432.q.144.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.r1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.U', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387455
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.S', '72.CH', '72.CQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4558, -1, 5193, -1], 'generators': [4103606723880, 16703, 6227393890, 1313941668480, 4103734078087, 87091216, 4103734078096], 'label': '18432.q.144.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.s1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.V', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387456
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.W', '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': ['72.B', '72.C', '72.N'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6887, -1, 6537, -1], 'generators': [127387560, 87102720, 20835531390117, 5167, 11520, 2789792409600, 7], 'label': '18432.q.144.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.t1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.W', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387457
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.B', '72.O', '72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6627, -1, 5872, -1], 'generators': [16703, 6227384421, 127387560, 87102720, 11543, 11520, 1313941668480], 'label': '18432.q.144.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.u1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.X', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387458
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.C', '72.O', '72.CQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6644, -1, 5913, -1], 'generators': [16703, 127387560, 87102720, 4097506704610, 11543, 11520, 1313941668480], 'label': '18432.q.144.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.v1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.Y', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387459
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Q', '72.CP', '72.CQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4291, -1, 4989, -1], 'generators': [16703, 127387560, 87102720, 11543, 4097506695141, 11520, 1313941668480], 'label': '18432.q.144.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.w1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.Z', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387460
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.D', '72.R', '72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5307, -1, 6217, -1], 'generators': [16703, 6227384421, 127387560, 16, 1313941668480, 87091216, 7], 'label': '18432.q.144.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '144.x1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BA', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 63387461
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.E', '72.R', '72.CQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5344, -1, 6234, -1], 'generators': [16703, 127387560, 16, 4097506704610, 1313941668480, 87091216, 7], 'label': '18432.q.144.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '144.y1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BB', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 63387462
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.S', '72.CP', '72.CQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4275, -1, 4933, -1], 'generators': [16703, 127387560, 16, 4097506695141, 1313941668480, 87091216, 7], 'label': '18432.q.144.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.z1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BC', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387463
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Z'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5819, -1, 5686, -1], 'generators': [20835531393818, 11543, 4103606712376, 5167, 2789792409600, 87091216, 4103734078096], 'label': '18432.q.144.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.Z', 'old_label': '144.ba1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BD', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387464
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '24.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.C'], 'contains': ['48.J', '48.L', '48.N', '48.P', '48.Q', '48.R', '48.T', '72.CM', '96.BO'], 'core': '18432.a1', 'coset_action_label': '24T12442', 'count': 12, 'diagramx': [442, -1, 1332, -1], 'generators': [5606275030426, 40284840, 7, 843, 11536, 4097506695141, 5167, 16, 1313941668480], 'label': '18432.q.24.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '24.b1', 'projective_image': '18432.q', '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': '768.1089108'}
  • id: 63387465
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.T'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9022, -1, 9360, -1], 'generators': [16703, 4103734078080, 1313988485176, 11527, 11300123081647, 87181935981, 9709968828818], 'label': '18432.q.144.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.T', 'old_label': '144.bb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BE', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387466
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.T'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9048, -1, 9384, -1], 'generators': [16703, 4103734078080, 1313988485176, 11527, 8396027169829, 11300123081647, 87181935981], 'label': '18432.q.144.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.T', 'old_label': '144.bc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BF', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387467
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Z'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5895, -1, 5639, -1], 'generators': [11543, 4103646998400, 11520, 5167, 4103606712376, 2789792409600, 20835531393818], 'label': '18432.q.144.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.Z', 'old_label': '144.bd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BG', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387468
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9718, -1, 9727, -1], 'generators': [23, 16703, 4103734078080, 127387560, 8396027169829, 11300123076480, 87181935981], 'label': '18432.q.144.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.BB', 'old_label': '144.be1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BH', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 63387469
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9636, -1, 9667, -1], 'generators': [9709968838309, 23, 11300123081647, 127387560, 1482078131290, 16703, 4103734078080], 'label': '18432.q.144.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.BC', 'old_label': '144.bf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BI', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 63387470
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.F', '72.G', '72.N'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6862, -1, 7129, -1], 'generators': [127387560, 20835531390117, 4103646986896, 5167, 2789792409600, 4103734078096, 7], 'label': '18432.q.144.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.bg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BJ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387471
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.F', '72.O', '72.CH'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6608, -1, 5983, -1], 'generators': [16703, 6227384421, 87102720, 4103606712376, 1313941668480, 4103734078087, 4103734078096], 'label': '18432.q.144.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.bh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BK', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387472
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.G', '72.O', '72.CI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6587, -1, 6002, -1], 'generators': [16703, 87102720, 4097506704610, 4103606712376, 1313941668480, 4103734078087, 4103734078096], 'label': '18432.q.144.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.bi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BL', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387473
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Q', '72.CH', '72.CI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4627, -1, 5409, -1], 'generators': [16703, 87102720, 4103606712376, 4097506695141, 1313941668480, 4103734078087, 4103734078096], 'label': '18432.q.144.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.bj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BM', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387474
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.BN', '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': ['72.B', '72.G', '72.BK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6947, -1, 7075, -1], 'generators': [180591228737, 20835531393818, 4103606712376, 5167, 2789792409600, 87091200, 7], 'label': '18432.q.144.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.bk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BN', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387475
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.C'], 'contains': ['48.K', '48.L', '48.O', '48.P', '48.W', '48.X', '48.Y', '72.CN', '96.BA'], 'core': '18432.a1', 'coset_action_label': '24T12450', 'count': 12, 'diagramx': [404, -1, 1263, -1], 'generators': [16, 7, 843, 4097506695141, 5167, 4103693803560, 11536, 1313941668480, 9709928549146], 'label': '18432.q.24.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '24.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.C', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387476
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.BO', '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': ['72.C', '72.F', '72.BK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6821, -1, 7057, -1], 'generators': [127387560, 3923142859457, 20835531390117, 5167, 2789792409600, 87091200, 7], 'label': '18432.q.144.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.bl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BO', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387477
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.B', '72.F', '72.BL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6986, -1, 7212, -1], 'generators': [180591228721, 127387560, 5167, 2789792409600, 87091200, 18301133928218, 7], 'label': '18432.q.144.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.bm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BP', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387478
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.C', '72.G', '72.BL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7459, -1, 7248, -1], 'generators': [127387560, 5167, 2789792409600, 3923142870977, 87091200, 18301133928218, 7], 'label': '18432.q.144.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.bn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BQ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387479
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.B', '72.F', '72.BO'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6967, -1, 7194, -1], 'generators': [180591228721, 20835531393818, 4103606712376, 5167, 2789792409600, 87091200, 7], 'label': '18432.q.144.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.bo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BR', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387480
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.C', '72.G', '72.BO'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7401, -1, 7230, -1], 'generators': [20835531393818, 4103606712376, 5167, 2789792409600, 3923142870977, 87091200, 7], 'label': '18432.q.144.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.bp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BS', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387481
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.H', '72.R', '72.CH'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5326, -1, 6251, -1], 'generators': [16703, 6227384421, 4103734089623, 4103734089600, 4103606712376, 1313941668480, 87091216], 'label': '18432.q.144.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '144.bq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BT', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 63387482
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.I', '72.R', '72.CI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5362, -1, 6269, -1], 'generators': [16703, 4103734089623, 4097506704610, 4103734089600, 4103606712376, 1313941668480, 87091216], 'label': '18432.q.144.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '144.br1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BU', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 63387483
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.S', '72.CH', '72.CI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4539, -1, 5260, -1], 'generators': [16703, 4103734089623, 4103734089600, 4103606712376, 4097506695141, 1313941668480, 87091216], 'label': '18432.q.144.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.bs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BV', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387484
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.D', '72.H', '72.BY'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5466, -1, 7441, -1], 'generators': [4103606723880, 11219048432047, 6227383801, 5167, 1313941668480, 4103646998400, 7], 'label': '18432.q.144.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.D', 'old_label': '144.bt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BW', 'subgroup_fusion': None, 'weyl_group': '128.513'}
  • id: 63387485
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.D', '72.H', '72.CA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5442, -1, 7391, -1], 'generators': [4103606723880, 6227383801, 5167, 1313941668480, 11219135529616, 4103646998400, 7], 'label': '18432.q.144.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.D', 'old_label': '144.bu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BX', 'subgroup_fusion': None, 'weyl_group': '128.513'}
  • id: 63387486
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.C'], 'contains': ['48.I', '48.J', '48.M', '48.N', '48.V', '48.W', '48.X', '72.CO', '96.BB'], 'core': '18432.a1', 'coset_action_label': '24T12448', 'count': 12, 'diagramx': [478, -1, 1153, -1], 'generators': [5606275030426, 16, 7, 843, 4097506695141, 4103693803560, 5167, 11536, 1313941668480], 'label': '18432.q.24.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '24.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.D', 'subgroup_fusion': None, 'weyl_group': '768.1089108'}
  • id: 63387487
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.E', '72.I', '72.BZ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5615, -1, 7534, -1], 'generators': [4103606723880, 11219048438416, 4097506706057, 5167, 1313941668480, 4103646998400, 7], 'label': '18432.q.144.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '144.bv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BY', 'subgroup_fusion': None, 'weyl_group': '128.513'}
  • id: 63387488
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.E', '72.I', '72.CA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5563, -1, 7504, -1], 'generators': [4097506706057, 5167, 1313941668480, 127376056, 11219135529616, 87091216, 7], 'label': '18432.q.144.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '144.bw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.BZ', 'subgroup_fusion': None, 'weyl_group': '128.513'}
  • id: 63387489
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.J', '72.BB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9784, -1, 9807, -1], 'generators': [16703, 4103734078080, 127387560, 11300123076480, 87181935981, 1313941680007, 9709968828818], 'label': '18432.q.144.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '144.bx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CA', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387490
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.J', '72.BC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9741, -1, 9785, -1], 'generators': [1313941680007, 127387560, 11300123081647, 16703, 4103734078080, 8396027160338, 1482078131290], 'label': '18432.q.144.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '144.by1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CB', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387491
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.K', '72.BB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9765, -1, 9745, -1], 'generators': [16703, 4103734078080, 127387560, 8396027169829, 11300123076480, 87181935981, 1313941680007], 'label': '18432.q.144.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '144.bz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CC', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387492
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.K', '72.BC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9697, -1, 9707, -1], 'generators': [1313941680007, 127387560, 11300123081647, 9709968838309, 16703, 4103734078080, 1482078131290], 'label': '18432.q.144.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '144.ca1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CD', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387493
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.J', '72.K', '72.BD'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9838, -1, 9884, -1], 'generators': [6920263510429, 16703, 1313941680007, 87181935981, 11300123076480, 127387560, 4103734078080], 'label': '18432.q.144.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '144.cb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CE', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387494
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.J', '72.K', '72.BE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9808, -1, 9857, -1], 'generators': [16703, 1313941680007, 11300123081647, 127387560, 1482078131290, 4103734078080, 6920263519898], 'label': '18432.q.144.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '144.cc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CF', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387495
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.J', '72.K', '72.BL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9890, -1, 9763, -1], 'generators': [4103734089623, 4103606712376, 5167, 2789792409600, 3923142870977, 4103646998416, 18301133928218], 'label': '18432.q.144.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '144.cd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CG', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 63387496
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BM', '72.CD', '72.CE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7847, -1, 8926, -1], 'generators': [16703, 9709881747098, 87102720, 4097506704610, 1313941668480, 127376040, 4103606723887], 'label': '18432.q.144.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.ce1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CH', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387497
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.A', '18.G', '32.G', '32.H'], 'core': '2.C', 'coset_action_label': None, 'count': 1, 'diagramx': [4704, 1706, 3988, 1770], 'generators': [11536, 16, 843, 127387560, 11219135523247, 4103734078080, 5167, 7, 1313941668480, 87102720, 93409310300, 6227384421], 'label': '18432.q.2.C', 'mobius_quo': 0, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.A'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.C', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 63387498
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I'], 'contains': ['48.B', '48.E', '48.S', '48.U', '48.BA', '72.CP', '96.A', '96.C', '96.Y'], 'core': '18432.a1', 'coset_action_label': '24T12242', 'count': 12, 'diagramx': [3614, -1, 1921, -1], 'generators': [11536, 16, 843, 127387560, 5167, 7, 1313941668480, 87102720, 6227384421], 'label': '18432.q.24.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '24.e1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.E', 'subgroup_fusion': None, 'weyl_group': '384.20163'}
  • id: 63387499
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BN', '72.CD', '72.CE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7809, -1, 8774, -1], 'generators': [16703, 87102720, 5606321841949, 4097506695141, 1313941668480, 127376040, 4103606723887], 'label': '18432.q.144.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.cf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CI', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387500
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.J', '72.BM', '72.CE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9548, -1, 9566, -1], 'generators': [16703, 87102720, 4097506704610, 9709881737629, 1313941668480, 127376040, 4103606723887], 'label': '18432.q.144.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.cg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CJ', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387501
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.L', '72.BN', '72.CE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7594, -1, 8870, -1], 'generators': [16703, 87102720, 9709881737629, 4097506695141, 1313941668480, 127376040, 4103606723887], 'label': '18432.q.144.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '144.ch1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CK', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387502
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.K', '72.BM', '72.CD'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9567, -1, 9584, -1], 'generators': [16703, 87102720, 4097506704610, 5606321851418, 1313941668480, 127376040, 4103606723887], 'label': '18432.q.144.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.ci1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CL', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387503
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.CM', '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': ['72.J', '72.K', '72.BQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9866, -1, 9830, -1], 'generators': [11219048438416, 4097506706057, 4103734089623, 4103606712376, 4103646986896, 5167, 1313941668480], 'label': '18432.q.144.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '144.cj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CM', 'subgroup_fusion': None, 'weyl_group': '128.1758'}
  • id: 63387504
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.CN', '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': ['72.M', '72.BN', '72.CD'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7613, -1, 8962, -1], 'generators': [16703, 87102720, 5606321851418, 4097506695141, 1313941668480, 127376040, 4103606723887], 'label': '18432.q.144.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '144.ck1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CN', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387505
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.CO', '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': ['72.L', '72.M', '72.BS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7500, -1, 8888, -1], 'generators': [4103734089623, 4103646998416, 180591240257, 5167, 4103606712376, 2789792409600, 20835531393818], 'label': '18432.q.144.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.H', 'old_label': '144.cl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CO', 'subgroup_fusion': None, 'weyl_group': '128.236'}
  • id: 63387506
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.CP', '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': ['72.L', '72.M', '72.BT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7520, -1, 8907, -1], 'generators': [6227395337, 4103734089623, 4103646986896, 4103606712376, 5167, 1313941668480, 11219135529616], 'label': '18432.q.144.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.H', 'old_label': '144.cm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CP', 'subgroup_fusion': None, 'weyl_group': '128.859'}
  • id: 63387507
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.CQ', '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': ['72.BW', '72.CD', '72.CE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7866, -1, 8810, -1], 'generators': [16703, 6227384421, 9709881747098, 4103606712360, 1313941668480, 4103646998400, 127387567], 'label': '18432.q.144.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.cn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CQ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387508
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.CR', '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': ['72.BX', '72.CD', '72.CE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7886, -1, 8738, -1], 'generators': [16703, 6227393890, 5606321841949, 4103606712360, 1313941668480, 4103646998400, 127387567], 'label': '18432.q.144.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.co1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CR', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387509
    {'ambient': '18432.q', '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': 1, 'contained_in': ['12.I'], 'contains': ['48.T', '48.U', '48.BA', '72.CQ', '96.B', '96.D', '96.Z'], 'core': '18432.a1', 'coset_action_label': '24T12243', 'count': 12, 'diagramx': [3587, -1, 1892, -1], 'generators': [127387560, 7, 843, 11536, 4097506695141, 5167, 87102720, 16, 1313941668480], 'label': '18432.q.24.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '24.f1', 'projective_image': '18432.q', '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': '384.20163'}
  • id: 63387510
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BW', '72.CE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8109, -1, 8828, -1], 'generators': [16703, 6227384421, 9709881737629, 4103606712360, 1313941668480, 4103646998400, 127387567], 'label': '18432.q.144.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.cp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CS', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387511
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BX', '72.CE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7828, -1, 8637, -1], 'generators': [16703, 6227393890, 9709881737629, 4103606712360, 1313941668480, 4103646998400, 127387567], 'label': '18432.q.144.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.cq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CT', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387512
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.BW', '72.CD'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8128, -1, 8944, -1], 'generators': [16703, 6227384421, 5606321851418, 4103606712360, 1313941668480, 4103646998400, 127387567], 'label': '18432.q.144.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.cr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387513
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BX', '72.CD'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7949, -1, 8756, -1], 'generators': [16703, 6227393890, 5606321851418, 4103606712360, 1313941668480, 4103646998400, 127387567], 'label': '18432.q.144.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.cs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CV', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387514
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.T'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9077, -1, 9434, -1], 'generators': [16703, 4103734078080, 1482078131290, 1313941668503, 1313988485176, 11300123076480, 8396027160338], 'label': '18432.q.144.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.T', 'old_label': '144.ct1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CW', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387515
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.T'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9130, -1, 9462, -1], 'generators': [9709968838309, 16703, 11300123076480, 1313988485176, 1313941668503, 1482078131290, 4103734078080], 'label': '18432.q.144.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.T', 'old_label': '144.ct2', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CX', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387516
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.CY', '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': ['72.DJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [6432, -1, 6351, -1], 'generators': [87102736, 5160, 4103734083247, 127382407, 11536, 1313941668480, 16906237719717], 'label': '18432.q.144.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DJ', 'old_label': '144.cu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CY', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387517
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.DK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4192, -1, 4810, -1], 'generators': [127387576, 127387567, 4103734083247, 87102720, 4103734089616, 1313941668480, 5606321841949], 'label': '18432.q.144.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DK', 'old_label': '144.cv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.CZ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387518
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.DA', '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': ['72.N', '72.Z', '72.DJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6105, -1, 6032, -1], 'generators': [127387560, 16906237719717, 4103734083247, 1313941668480, 87107903, 11536, 7], 'label': '18432.q.144.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.cw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DA', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387519
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.DB', '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': ['72.P', '72.BA', '72.DJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6040, -1, 6290, -1], 'generators': [18301133924517, 127387560, 4103734083247, 1313941668480, 87107903, 11536, 7], 'label': '18432.q.144.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.cx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DB', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387520
    {'ambient': '18432.q', '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': 1, 'contained_in': ['12.G'], 'contains': ['48.D', '48.F', '48.V', '48.Z', '48.BB', '72.CR', '96.BC'], 'core': '18432.a1', 'coset_action_label': '24T12246', 'count': 12, 'diagramx': [2033, -1, 620, -1], 'generators': [16703, 7, 1313941668480, 5183, 127382407, 87102720, 4103734078080, 174363856696, 5606321841949], 'label': '18432.q.24.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '24.g1', 'projective_image': '18432.q', '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': '384.18158'}
  • id: 63387521
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.DC', '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': ['72.P', '72.Z', '72.DN'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5964, -1, 5804, -1], 'generators': [127387560, 87102736, 4103734083247, 1313941668480, 19440635185317, 5160, 11536], 'label': '18432.q.144.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.cy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DC', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387522
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.DD', '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': ['72.N', '72.BA', '72.DN'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6017, -1, 5854, -1], 'generators': [127387560, 20835531390117, 87102736, 4103734083247, 1313941668480, 5160, 11536], 'label': '18432.q.144.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.cz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DD', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387523
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7556, -1, 8489, -1], 'generators': [6227384421, 40284847, 4103734089616, 4103734083247, 40284856, 1313941668480, 9709928558626], 'label': '18432.q.144.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DA', 'old_label': '144.da1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DE', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 63387524
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.DE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3315, -1, 4055, -1], 'generators': [40284856, 4103734083247, 4103734089616, 40279680, 1313941668480, 9709928549146, 6354044781], 'label': '18432.q.144.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DE', 'old_label': '144.db1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DF', 'subgroup_fusion': None, 'weyl_group': '64.56'}
  • id: 63387525
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.O', '72.R', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5238, -1, 5761, -1], 'generators': [40284840, 6227384421, 4103734083247, 4103734089616, 5183, 1313941668480, 5160], 'label': '18432.q.144.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.dc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DG', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387526
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.O', '72.S', '72.DW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4608, -1, 5151, -1], 'generators': [16, 40279687, 4103734083247, 4103734089616, 1313941668480, 6354039013, 7], 'label': '18432.q.144.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.dd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DH', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387527
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Q', '72.R', '72.DW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5019, -1, 5595, -1], 'generators': [16, 40279687, 4103734083247, 4103734089616, 1313941668480, 6354044781, 7], 'label': '18432.q.144.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.de1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DI', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387528
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.DJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.Q', '72.S', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4577, -1, 5118, -1], 'generators': [40284840, 4103734083247, 4103734089616, 6227390173, 5183, 1313941668480, 5160], 'label': '18432.q.144.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.df1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DJ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387529
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2621, -1, 2264, -1], 'generators': [87102720, 7, 5183, 4103734089616, 4103734083247, 2789792409600, 5606321847717], 'label': '18432.q.144.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DR', 'old_label': '144.dg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DK', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387530
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2708, -1, 3855, -1], 'generators': [40284840, 6227384421, 16, 4103734083247, 4103734089616, 1313941668480, 7], 'label': '18432.q.144.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DT', 'old_label': '144.dh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DL', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387531
    {'ambient': '18432.q', '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': 1, 'contained_in': ['12.G'], 'contains': ['48.Y', '48.Z', '48.BB', '72.CS', '96.BD'], 'core': '18432.a1', 'coset_action_label': '24T12247', 'count': 12, 'diagramx': [2002, -1, 816, -1], 'generators': [16703, 7, 1313941668480, 5183, 127382407, 87102720, 4103734078080, 174363856696, 5606321847717], 'label': '18432.q.24.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '24.h1', 'projective_image': '18432.q', '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': '384.18158'}
  • id: 63387532
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.DM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.A', '72.N', '72.O', '72.P', '72.Q'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6076, -1, 5791, -1], 'generators': [127387560, 16, 87102720, 4103734083247, 1313941668480, 5160, 11536], 'label': '18432.q.144.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.di1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DM', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63387533
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.DN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.A', '72.R', '72.S'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4592, -1, 5352, -1], 'generators': [16, 87102720, 127382407, 4103734083247, 1313941668480, 11536, 7], 'label': '18432.q.144.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '144.dj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DN', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 63387534
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.X', '72.Y', '72.CV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8507, -1, 8237, -1], 'generators': [87102736, 4103734089616, 5167, 2789792409600, 3923142870977, 4103734078087, 18301133928218], 'label': '18432.q.144.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.dk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DO', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387535
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.DP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.X', '72.Y', '72.CW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8488, -1, 8038, -1], 'generators': [18301133924517, 180703353737, 87102736, 4103734089616, 5167, 2789792409600, 4103734078087], 'label': '18432.q.144.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.dl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DP', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387536
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.T', '72.Y', '72.CV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8925, -1, 9016, -1], 'generators': [18301133924517, 87102736, 4103734089616, 5167, 180591240257, 2789792409600, 4103734078087], 'label': '18432.q.144.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.dm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DQ', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387537
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.U', '72.Y', '72.CW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8826, -1, 7887, -1], 'generators': [18301133924517, 3923030724617, 87102736, 4103734089616, 5167, 2789792409600, 4103734078087], 'label': '18432.q.144.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '144.dn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DR', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387538
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.T', '72.V', '72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8982, -1, 9171, -1], 'generators': [6227384421, 40284847, 4103734089616, 4103734083247, 40279703, 1313941668480, 9709928558626], 'label': '18432.q.144.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.do1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DS', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 63387539
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.V', '72.X', '72.CV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8963, -1, 8998, -1], 'generators': [87102736, 4103734089616, 5167, 180591240257, 2789792409600, 4103734078087, 18301133928218], 'label': '18432.q.144.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.dp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DT', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387540
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.T', '72.V', '72.DD'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9159, -1, 9270, -1], 'generators': [40284840, 11219048438416, 4103734089616, 6227383801, 5167, 1313941668480, 4103734078087], 'label': '18432.q.144.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.dq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DU', 'subgroup_fusion': None, 'weyl_group': '128.1758'}
  • id: 63387541
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.U', '72.W', '72.DF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8788, -1, 7697, -1], 'generators': [40279703, 4103734083247, 4103734089616, 1313941668480, 9709928549146, 40284847, 6354044770], 'label': '18432.q.144.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.M', 'old_label': '144.dr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DV', 'subgroup_fusion': None, 'weyl_group': '128.236'}
  • id: 63387542
    {'ambient': '18432.q', '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': 1, 'contained_in': ['12.C'], 'contains': ['48.I', '48.J', '48.O', '48.P', '48.BG', '48.BL', '48.BN', '72.DP', '96.CA'], 'core': '1152.A', 'coset_action_label': None, 'count': 12, 'diagramx': [223, -1, 1352, -1], 'generators': [4103734078080, 6227384421, 16, 5167, 1313941668480, 9709928549146, 11536, 843, 7], 'label': '18432.q.24.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '24.i1', 'projective_image': '18432.q', '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': '768.1089108'}
  • id: 63387543
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.W', '72.X', '72.CW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8769, -1, 7751, -1], 'generators': [3923030724617, 87102736, 4103734089616, 5167, 2789792409600, 4103734078087, 18301133928218], 'label': '18432.q.144.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '144.ds1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DW', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387544
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.U', '72.W', '72.DI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8865, -1, 7827, -1], 'generators': [40284840, 4097380065841, 4103734089616, 5167, 1313941668480, 11219135529616, 4103734078087], 'label': '18432.q.144.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.M', 'old_label': '144.dt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DX', 'subgroup_fusion': None, 'weyl_group': '128.859'}
  • id: 63387545
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.X', '72.Y', '72.DJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8268, -1, 7788, -1], 'generators': [4103606723880, 87102736, 4103734089616, 5167, 2789792409600, 4103734078087, 18301133928218], 'label': '18432.q.144.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.du1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387546
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Y', '72.Z', '72.DJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6330, -1, 6488, -1], 'generators': [18301133924517, 127387560, 87102736, 4103734089616, 5167, 2789792409600, 4103734078087], 'label': '18432.q.144.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.dv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.DZ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387547
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.X', '72.Y', '72.DL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8293, -1, 7926, -1], 'generators': [87102720, 4103734083247, 4103734089616, 6227390173, 127382423, 1313941668480, 127387567], 'label': '18432.q.144.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.dw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EA', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387548
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.X', '72.BA', '72.DJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6458, -1, 6453, -1], 'generators': [127387560, 87102736, 4103734089616, 5167, 2789792409600, 4103734078087, 18301133928218], 'label': '18432.q.144.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.dx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EB', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387549
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Z', '72.BA', '72.DN'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5932, -1, 5744, -1], 'generators': [127387560, 20835531393818, 87102736, 4103734089616, 5167, 2789792409600, 4103734078087], 'label': '18432.q.144.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.dy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EC', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387550
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2541, -1, 2287, -1], 'generators': [16, 5160, 4103734083247, 87102720, 4103734089616, 2789792409600, 5606321841949], 'label': '18432.q.144.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DR', 'old_label': '144.dz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ED', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387551
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.EE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.A'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4305, -1, 4641, -1], 'generators': [127387560, 16, 87102720, 4103734083247, 1313941668480, 11536, 7], 'label': '18432.q.144.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.A', 'old_label': '144.ea1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EE', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63387552
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.EF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.A', '72.Z', '72.BA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5776, -1, 5423, -1], 'generators': [127387560, 87102720, 4103734083247, 5183, 1313941668480, 11536, 7], 'label': '18432.q.144.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.eb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EF', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63387553
    {'ambient': '18432.q', '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': 1, 'contained_in': ['6.B', '8.B'], 'contains': ['48.BC', '48.BD', '48.BE', '48.BF', '48.BH', '48.BI', '48.BK', '72.DQ', '96.J'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2169, -1, 1529, -1], 'generators': [4103734078080, 5606321851429, 6227384402, 87102736, 5167, 1313941668480, 11536, 40284847, 843], 'label': '18432.q.24.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '24.j1', 'projective_image': '18432.q', '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': '384.18069'}
  • id: 63387554
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BJ', '72.BU', '72.CW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8724, -1, 7983, -1], 'generators': [180703353737, 4103734089616, 5167, 2789792409600, 4103646998416, 18301133928218, 7], 'label': '18432.q.144.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.ec1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EG', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387555
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BJ', '72.BV', '72.CV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8666, -1, 8382, -1], 'generators': [4103734089616, 5167, 180591240257, 2789792409600, 4103646998416, 18301133928218, 7], 'label': '18432.q.144.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.ed1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EH', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387556
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BB', '72.BC', '72.BD', '72.BE', '72.BL', '72.BU', '72.CV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9586, -1, 9548, -1], 'generators': [4103734089616, 5167, 2789792409600, 3923142870977, 4103646998416, 18301133928218, 7], 'label': '18432.q.144.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.ee1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EI', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387557
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BL', '72.BV', '72.CW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8705, -1, 7869, -1], 'generators': [3923030724617, 4103734089616, 5167, 2789792409600, 4103646998416, 18301133928218, 7], 'label': '18432.q.144.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '144.ef1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EJ', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387558
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BM', '72.BX', '72.CY'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8051, -1, 8564, -1], 'generators': [5606321847717, 40279703, 4103734083247, 4103734089616, 40279680, 1313941668480, 6354039002], 'label': '18432.q.144.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.eg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EK', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387559
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BN', '72.BW', '72.CY'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7632, -1, 8792, -1], 'generators': [40279703, 6354044770, 40279680, 4103734083247, 4103734089616, 1313941668480, 5606321841949], 'label': '18432.q.144.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.eh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EL', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387560
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BB', '72.BC', '72.BF', '72.BG', '72.BM', '72.BW', '72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9528, -1, 9530, -1], 'generators': [6227384421, 40279680, 4103734089616, 4103734083247, 40279703, 1313941668480, 9709928558626], 'label': '18432.q.144.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.ei1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EM', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387561
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BN', '72.BX', '72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7790, -1, 8600, -1], 'generators': [40279703, 40279680, 6227390173, 4103734083247, 4103734089616, 1313941668480, 9709928558626], 'label': '18432.q.144.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '144.ej1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EN', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387562
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BF', '72.BG', '72.BH', '72.BI', '72.BP', '72.BU', '72.CV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9468, -1, 9512, -1], 'generators': [18301133924517, 4103734089616, 5167, 2789792409600, 3923142870977, 4103646998416, 7], 'label': '18432.q.144.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.ek1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EO', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387563
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BD', '72.BE', '72.BH', '72.BI', '72.BM', '72.BW', '72.DC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9676, -1, 9647, -1], 'generators': [6227384421, 40279680, 4103734083247, 40279703, 4103734089616, 1313941668480, 5606321841949], 'label': '18432.q.144.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.el1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EP', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387564
    {'ambient': '18432.q', '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': 1, 'contained_in': ['8.B', '12.C'], 'contains': ['48.K', '48.L', '48.M', '48.N', '48.BG', '48.BJ', '48.BL', '72.DQ', '96.CB'], 'core': '1152.A', 'coset_action_label': None, 'count': 12, 'diagramx': [532, -1, 1176, -1], 'generators': [4103734078080, 6227384421, 16, 5167, 1313941668480, 11536, 8396027160338, 843, 7], 'label': '18432.q.24.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '24.k1', 'projective_image': '18432.q', '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': '768.1089108'}
  • id: 63387565
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BB', '72.BD', '72.BF', '72.BH', '72.BQ', '72.BY', '72.DD'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9657, -1, 9688, -1], 'generators': [40284840, 11219048432047, 4103734089616, 6227383801, 5167, 1313941668480, 7], 'label': '18432.q.144.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.em1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EQ', 'subgroup_fusion': None, 'weyl_group': '256.16883'}
  • id: 63387566
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BC', '72.BE', '72.BG', '72.BI', '72.BQ', '72.BZ', '72.DD'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9610, -1, 9625, -1], 'generators': [40284840, 11219048438416, 4103734089616, 6227383801, 5167, 1313941668480, 7], 'label': '18432.q.144.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.en1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ER', 'subgroup_fusion': None, 'weyl_group': '256.16883'}
  • id: 63387567
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BP', '72.BV', '72.CW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8686, -1, 8092, -1], 'generators': [18301133924517, 3923030724617, 4103734089616, 5167, 2789792409600, 4103646998416, 7], 'label': '18432.q.144.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '144.eo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ES', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387568
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BT', '72.CA', '72.DI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7745, -1, 8357, -1], 'generators': [40284840, 4097380065841, 4103734089616, 5167, 1313941668480, 11219135523247, 7], 'label': '18432.q.144.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.V', 'old_label': '144.ep1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ET', 'subgroup_fusion': None, 'weyl_group': '128.513'}
  • id: 63387569
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BN', '72.BX', '72.DC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7993, -1, 8618, -1], 'generators': [40279703, 40279680, 6227390173, 4103734083247, 4103734089616, 1313941668480, 5606321847717], 'label': '18432.q.144.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '144.eq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EU', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387570
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.N', '72.BJ', '72.BK', '72.BL', '72.DJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6769, -1, 7163, -1], 'generators': [127387560, 4103734089616, 5167, 2789792409600, 4103646998416, 18301133928218, 7], 'label': '18432.q.144.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.er1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EV', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387571
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BM', '72.BN', '72.DK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7671, -1, 8849, -1], 'generators': [87102720, 127382400, 127382423, 4103734089616, 4103734083247, 1313941668480, 5606321847717], 'label': '18432.q.144.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.es1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387572
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.O', '72.BL', '72.BM', '72.BO', '72.BP', '72.BQ', '72.DL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8147, -1, 7715, -1], 'generators': [6227384421, 87102720, 4103734083247, 4103734089616, 127382423, 127382400, 1313941668480], 'label': '18432.q.144.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.et1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EX', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 63387573
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.EY', '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': ['72.N', '72.P', '72.BK', '72.BO', '72.BR', '72.BS', '72.DN'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6518, -1, 7110, -1], 'generators': [127387560, 20835531393818, 4103734089616, 5167, 2789792409600, 4103646998416, 7], 'label': '18432.q.144.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.eu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EY', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387574
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.P', '72.BJ', '72.BP', '72.BR', '72.DJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6539, -1, 7306, -1], 'generators': [18301133924517, 127387560, 4103734089616, 5167, 2789792409600, 4103646998416, 7], 'label': '18432.q.144.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.ev1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.EZ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387575
    {'ambient': '18432.q', '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': 1, 'contained_in': ['12.A', '12.C', '12.G'], 'contains': ['48.Q', '48.V', '48.Y', '48.BG', '48.BO', '72.DS', '96.BP'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [847, -1, 1308, -1], 'generators': [174363856680, 87102727, 11536, 1313941668480, 5167, 87102736, 127387560, 4103734078080, 5606321851429], 'label': '18432.q.24.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.l1', 'projective_image': '18432.q', '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': '768.1087582'}
  • id: 63387576
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Q', '72.BJ', '72.BN', '72.BS', '72.BT', '72.DL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7575, -1, 7661, -1], 'generators': [87102720, 127382400, 127382423, 6227390173, 4103734089616, 4103734083247, 1313941668480], 'label': '18432.q.144.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.ew1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FA', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 63387577
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.O', '72.Q', '72.BK', '72.BR', '72.DO'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6500, -1, 6152, -1], 'generators': [87102720, 127382400, 6227390162, 127382423, 4103734089616, 4103734083247, 1313941668480], 'label': '18432.q.144.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.ex1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FB', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387578
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BU', '72.BV', '72.DJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8568, -1, 8294, -1], 'generators': [18301133924517, 4103606723880, 4103734089616, 5167, 2789792409600, 4103646998416, 7], 'label': '18432.q.144.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.ey1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FC', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387579
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BW', '72.BX', '72.DK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7971, -1, 8525, -1], 'generators': [127387576, 127387567, 87107887, 4103734089616, 4103734083247, 1313941668480, 5606321847717], 'label': '18432.q.144.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.ez1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FD', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387580
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.R', '72.BU', '72.BW', '72.BY', '72.BZ', '72.CA', '72.DL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8090, -1, 7679, -1], 'generators': [6227384421, 127387576, 4103734083247, 4103734089616, 87107887, 1313941668480, 127387567], 'label': '18432.q.144.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.fa1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FE', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 63387581
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.S', '72.BV', '72.BX', '72.DL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8031, -1, 7947, -1], 'generators': [127387576, 4103734083247, 4103734089616, 6227390173, 87107887, 1313941668480, 127387567], 'label': '18432.q.144.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.fb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FF', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 63387582
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.R', '72.S', '72.DO'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4519, -1, 5438, -1], 'generators': [6227384410, 127387567, 87107887, 4103734089616, 4103734083247, 127387576, 1313941668480], 'label': '18432.q.144.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '144.fc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FG', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 63387583
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.T', '72.BB', '72.DX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9264, -1, 9602, -1], 'generators': [4103734078080, 127387560, 87181920741, 8396027160338, 13834520547263, 1313941673647, 1313941680016], 'label': '18432.q.144.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.fd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FH', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387584
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.T', '72.BC', '72.DX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9414, -1, 9297, -1], 'generators': [4103734078080, 127387560, 8396027166106, 87181920741, 15229329660863, 1313941673647, 1313941680016], 'label': '18432.q.144.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.fe1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FI', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387585
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.V', '72.BB', '72.DZ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9487, -1, 9340, -1], 'generators': [4103734078080, 127387560, 12694932195247, 8396027166106, 87181920722, 1313941673647, 1313941680016], 'label': '18432.q.144.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.ff1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FJ', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387586
    {'ambient': '18432.q', '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': 1, 'contained_in': ['12.B', '12.C', '12.H'], 'contains': ['48.R', '48.W', '48.BJ', '48.BN', '48.BO', '72.DR', '96.H', '96.BQ'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [875, -1, 1240, -1], 'generators': [4103734078080, 16, 87102720, 5606321841949, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.24.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.m1', 'projective_image': '18432.q', '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': '768.1087581'}
  • id: 63387587
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.V', '72.BC', '72.DZ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9508, -1, 9321, -1], 'generators': [8396027160338, 127387560, 1313941673647, 87181920722, 11300123081647, 1313941680016, 4103734078080], 'label': '18432.q.144.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.fg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FK', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387588
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.V', '72.BF', '72.DX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9288, -1, 9243, -1], 'generators': [8396027166106, 127387560, 1313941673647, 13834520547263, 87181920741, 1313941680016, 4103734078080], 'label': '18432.q.144.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.fh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FL', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387589
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.V', '72.BG', '72.DX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9213, -1, 9219, -1], 'generators': [4103734078080, 127387560, 87181920741, 15229329660863, 8396027160338, 1313941673647, 1313941680016], 'label': '18432.q.144.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.fi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FM', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387590
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.T', '72.BF', '72.DZ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9443, -1, 9489, -1], 'generators': [4103734078080, 127387560, 12694932195247, 8396027160338, 87181920722, 1313941673647, 1313941680016], 'label': '18432.q.144.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.fj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FN', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387591
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.T', '72.BG', '72.DZ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9388, -1, 9409, -1], 'generators': [4103734078080, 127387560, 8396027166106, 11300123081647, 87181920722, 1313941673647, 1313941680016], 'label': '18432.q.144.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.fk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FO', 'subgroup_fusion': None, 'weyl_group': '256.25886'}
  • id: 63387592
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.X', '72.BL', '72.EB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8431, -1, 7906, -1], 'generators': [4103693803576, 4103734089616, 5167, 2789792409600, 3923142870977, 16906281269018, 127387567], 'label': '18432.q.144.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FP', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387593
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.Y', '72.BJ', '72.EB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8315, -1, 8056, -1], 'generators': [4103693803576, 4103734089616, 5167, 180591240257, 2789792409600, 16906281269018, 127387567], 'label': '18432.q.144.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FQ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387594
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.X', '72.BJ', '72.EC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8210, -1, 7733, -1], 'generators': [180591240262, 4103693803576, 4103734089616, 5167, 2789792409600, 16906281269018, 127387567], 'label': '18432.q.144.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FR', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387595
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Y', '72.BJ', '72.EC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8230, -1, 7808, -1], 'generators': [180591240262, 4103693803576, 16906281265317, 4103734089616, 5167, 2789792409600, 127387567], 'label': '18432.q.144.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FS', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387596
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Y', '72.BL', '72.EC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8247, -1, 7768, -1], 'generators': [4103693803576, 3923142870982, 4103734089616, 5167, 2789792409600, 16906281269018, 127387567], 'label': '18432.q.144.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FT', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387597
    {'ambient': '18432.q', '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.C', '12.D', '12.I'], 'contains': ['48.S', '48.T', '48.X', '48.BL', '48.BO', '72.DT', '96.E', '96.BR'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1933, -1, 1649, -1], 'generators': [40284840, 4103734078080, 6227384421, 16, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.24.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.n1', 'projective_image': '18432.q', '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': '768.1087581'}
  • id: 63387598
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Y', '72.BP', '72.EB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8391, -1, 8164, -1], 'generators': [4103693803576, 16906281265317, 4103734089616, 5167, 2789792409600, 3923142870977, 127387567], 'label': '18432.q.144.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387599
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.X', '72.BP', '72.EC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8372, -1, 8020, -1], 'generators': [4103693803576, 16906281265317, 3923142870982, 4103734089616, 5167, 2789792409600, 127387567], 'label': '18432.q.144.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FV', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387600
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.X', '72.BJ', '72.EB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8412, -1, 7965, -1], 'generators': [4103693803576, 16906281265317, 4103734089616, 5167, 180591240257, 2789792409600, 127387567], 'label': '18432.q.144.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FW', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387601
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.Y', '72.BU', '72.EB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8628, -1, 8315, -1], 'generators': [40284856, 4103734089616, 5167, 2789792409600, 3923142870977, 16906281269018, 4103606723887], 'label': '18432.q.144.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.ft1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FX', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387602
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.X', '72.BU', '72.EC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8469, -1, 8146, -1], 'generators': [40284856, 16906281265317, 3923142870982, 4103734089616, 5167, 2789792409600, 4103606723887], 'label': '18432.q.144.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FY', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387603
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.FZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.Y', '72.BV', '72.EB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8546, -1, 8255, -1], 'generators': [40284856, 4103734089616, 5167, 180591240257, 2789792409600, 16906281269018, 4103606723887], 'label': '18432.q.144.FZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.FZ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387604
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.X', '72.BV', '72.EC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8450, -1, 8110, -1], 'generators': [180591240262, 40284856, 16906281265317, 4103734089616, 5167, 2789792409600, 4103606723887], 'label': '18432.q.144.GA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GA', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387605
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.Y', '72.BU', '72.EC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8353, -1, 8182, -1], 'generators': [40284856, 3923142870982, 4103734089616, 5167, 2789792409600, 16906281269018, 4103606723887], 'label': '18432.q.144.GB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GB', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387606
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.Y', '72.BV', '72.EC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8334, -1, 8128, -1], 'generators': [180591240262, 40284856, 4103734089616, 5167, 2789792409600, 16906281269018, 4103606723887], 'label': '18432.q.144.GC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GC', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387607
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.X', '72.BU', '72.EB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8647, -1, 8273, -1], 'generators': [40284856, 16906281265317, 4103734089616, 5167, 2789792409600, 3923142870977, 4103606723887], 'label': '18432.q.144.GD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.fz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GD', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387608
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A', '2.B', '2.C'], 'contains': ['8.A', '12.I', '12.J', '16.A', '16.E'], 'core': '4.A', 'coset_action_label': None, 'count': 1, 'diagramx': [3988, 5186, 1857, 5382], 'generators': [11536, 16, 843, 127387560, 4103734078080, 5167, 7, 1313941668480, 87102720, 93409310300, 6227384421], 'label': '18432.q.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'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.A', 'subgroup_fusion': None, 'weyl_group': '40000.br'}
  • id: 63387609
    {'ambient': '18432.q', '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.B', '12.D', '12.G'], 'contains': ['48.Z', '48.BO', '72.DU', '96.BS'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1970, -1, 1442, -1], 'generators': [87102727, 4103734078080, 127387560, 87102736, 5606321841949, 174363856680, 5167, 1313941668480, 11536], 'label': '18432.q.24.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.o1', 'projective_image': '18432.q', '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': '768.1087582'}
  • id: 63387610
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.X', '72.BV', '72.EB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8527, -1, 8201, -1], 'generators': [40284856, 16906281265317, 4103734089616, 5167, 180591240257, 2789792409600, 4103606723887], 'label': '18432.q.144.GE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.ga1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GE', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387611
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.DX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9239, -1, 9106, -1], 'generators': [8396027166106, 87181926493, 1313941680016, 1313941673647, 13834520547263, 127382407, 4103734078080], 'label': '18432.q.144.GF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DX', 'old_label': '144.gb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GF', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387612
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9316, -1, 9149, -1], 'generators': [8396027160338, 87181926493, 1313941680016, 1313941673647, 13834520547263, 127382407, 4103734078080], 'label': '18432.q.144.GG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DX', 'old_label': '144.gb2', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GG', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387613
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CH'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4712, -1, 5526, -1], 'generators': [4103606723880, 6227384421, 5167, 2789792409616, 1314028771200, 11536, 4103734078087], 'label': '18432.q.144.GH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CH', 'old_label': '144.gc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GH', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387614
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4021, -1, 4266, -1], 'generators': [6227384421, 1314028771200, 5167, 1313941668496, 1313941668487, 127387560, 11536], 'label': '18432.q.144.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CP', 'old_label': '144.gd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GI', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387615
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2492, -1, 356, -1], 'generators': [4103734078080, 87102720, 5606321841949, 11520, 1313941668480, 127376056, 7], 'label': '18432.q.144.GJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CR', 'old_label': '144.ge1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GJ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387616
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4046, -1, 4290, -1], 'generators': [6227384421, 87102720, 1313941668487, 1313941668496, 5167, 11536, 1313988496680], 'label': '18432.q.144.GK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CP', 'old_label': '144.gf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GK', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387617
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2517, -1, 379, -1], 'generators': [4103734078080, 11543, 5606321851418, 1313941668480, 127376056, 87091216, 16687], 'label': '18432.q.144.GL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CR', 'old_label': '144.gg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GL', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387618
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['48.A', '48.B', '48.C', '72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3880, -1, 3140, -1], 'generators': [6227384421, 127387560, 16, 87102720, 5167, 11536, 7], 'label': '18432.q.144.GM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CP', 'old_label': '144.gh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GM', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387619
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['48.D', '72.CR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2200, -1, 222, -1], 'generators': [4103734078080, 16, 5606321851418, 1313941668480, 5160, 127376056, 87091216], 'label': '18432.q.144.GN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.G', 'old_label': '144.gi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GN', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 63387620
    {'ambient': '18432.q', '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.A', '12.D', '12.H'], 'contains': ['48.BN', '48.BO', '72.DV', '96.I', '96.BT'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [978, -1, 1468, -1], 'generators': [16, 7, 843, 5167, 87102720, 11536, 1313941668480, 4103734078080, 9709928549146], 'label': '18432.q.24.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.p1', 'projective_image': '18432.q', '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': '768.1087581'}
  • id: 63387621
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['48.E', '72.CP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3855, -1, 3116, -1], 'generators': [6227384421, 16, 5167, 1314028771200, 11536, 1313988496680, 7], 'label': '18432.q.144.GO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CP', 'old_label': '144.gj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GO', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387622
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.F', '48.G', '72.CR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2461, -1, 155, -1], 'generators': [4103734078080, 11543, 5606321851418, 87107887, 1313941668480, 127376056, 16687], 'label': '18432.q.144.GP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.G', 'old_label': '144.gk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GP', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 63387623
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['48.H', '72.CH'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4861, -1, 4952, -1], 'generators': [6227384421, 2789745614760, 2789792409607, 5167, 1314028771200, 11536, 4103734078096], 'label': '18432.q.144.GQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.CH', 'old_label': '144.gl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GQ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387624
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CL', '72.CU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1118, -1, 2979, -1], 'generators': [23, 40284840, 6227384421, 5167, 1313941668480, 9709928549146, 11536], 'label': '18432.q.144.GR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GR', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387625
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CG', '72.CL', '72.CT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1447, -1, 3322, -1], 'generators': [23, 40284840, 6227384421, 9709928554906, 5167, 1313941668480, 11536], 'label': '18432.q.144.GS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GS', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387626
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CF', '72.CM', '72.CU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1061, -1, 3340, -1], 'generators': [5606275030426, 23, 11536, 4097506695141, 5167, 40284840, 1313941668480], 'label': '18432.q.144.GT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.go1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GT', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387627
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CG', '72.CM', '72.CT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1428, -1, 3430, -1], 'generators': [23, 40284840, 5606275036186, 5167, 4097506695141, 1313941668480, 11536], 'label': '18432.q.144.GU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387628
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CG', '72.CL', '72.CU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1409, -1, 3521, -1], 'generators': [23, 40284840, 6227384421, 5606275030426, 5167, 1313941668480, 11536], 'label': '18432.q.144.GV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GV', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387629
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CG', '72.CM', '72.CU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1143, -1, 3611, -1], 'generators': [23, 11536, 4097506695141, 5167, 40284840, 1313941668480, 9709928549146], 'label': '18432.q.144.GW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GW', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387630
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CL', '72.CT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1022, -1, 2943, -1], 'generators': [23, 40284840, 6227384421, 5606275036186, 5167, 1313941668480, 11536], 'label': '18432.q.144.GX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GX', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387631
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.A', '12.B', '12.I'], 'contains': ['48.U', '48.BO', '72.DW', '96.F', '96.BU'], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3301, -1, 1728, -1], 'generators': [40284840, 4103734078080, 16, 5167, 1313941668480, 11536, 6354044781, 843, 7], 'label': '18432.q.24.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.q1', 'projective_image': '18432.q', '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': '768.1087581'}
  • id: 63387632
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CM', '72.CT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1041, -1, 3208, -1], 'generators': [23, 40284840, 9709928554906, 5167, 4097506695141, 1313941668480, 11536], 'label': '18432.q.144.GY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GY', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387633
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.GZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CB', '72.CN', '72.CU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1467, -1, 2925, -1], 'generators': [23, 6227384421, 4103693803560, 5606275030426, 5167, 1313941668480, 11536], 'label': '18432.q.144.GZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.GZ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387634
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CB', '72.CO', '72.CT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1656, -1, 2775, -1], 'generators': [23, 6227384421, 4103693803560, 9709928554906, 5167, 1313941668480, 11536], 'label': '18432.q.144.HA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HA', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387635
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CC', '72.CN', '72.CU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1554, -1, 3467, -1], 'generators': [23, 4103693803560, 5167, 4097506695141, 1313941668480, 9709928549146, 11536], 'label': '18432.q.144.HB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HB', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387636
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CC', '72.CO', '72.CT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1676, -1, 3226, -1], 'generators': [23, 5606275036186, 4103693803560, 5167, 4097506695141, 1313941668480, 11536], 'label': '18432.q.144.HC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HC', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387637
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CB', '72.CO', '72.CU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1486, -1, 2907, -1], 'generators': [23, 6227384421, 4103693803560, 5167, 1313941668480, 9709928549146, 11536], 'label': '18432.q.144.HD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HD', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387638
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CC', '72.CO', '72.CU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1505, -1, 3449, -1], 'generators': [23, 4103693803560, 5606275030426, 5167, 4097506695141, 1313941668480, 11536], 'label': '18432.q.144.HE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.gz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HE', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387639
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CB', '72.CN', '72.CT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1752, -1, 2793, -1], 'generators': [23, 6227384421, 5606275036186, 4103693803560, 5167, 1313941668480, 11536], 'label': '18432.q.144.HF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ha1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387640
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CC', '72.CN', '72.CT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1695, -1, 3244, -1], 'generators': [23, 4103693803560, 9709928554906, 5167, 4097506695141, 1313941668480, 11536], 'label': '18432.q.144.HG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HG', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387641
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CB', '72.CF', '72.DQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1821, -1, 2655, -1], 'generators': [6227384421, 5167, 1313941668480, 11536, 8396027160338, 4103734078087, 4103734078096], 'label': '18432.q.144.HH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HH', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387642
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '12.G', '12.H', '12.I'], 'contains': ['48.BA', '48.BB', '48.BO', '72.A', '96.N', '96.U', '96.BV'], 'core': '72.A', 'coset_action_label': None, 'count': 2, 'diagramx': [2837, -1, 1615, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.24.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '24.r1', 'projective_image': '18432.q', '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': '576.5126'}
  • id: 63387643
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CB', '72.CG', '72.DP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1181, -1, 2961, -1], 'generators': [6227384421, 5606275030426, 5167, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.HI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HI', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387644
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CC', '72.CF', '72.DQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1840, -1, 2829, -1], 'generators': [6920176419218, 5167, 4097506695141, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.HJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.he1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HJ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387645
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CC', '72.CG', '72.DP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1162, -1, 3376, -1], 'generators': [5167, 4097506695141, 1313941668480, 9709928549146, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.HK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HK', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387646
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CB', '72.CG', '72.DQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1802, -1, 2811, -1], 'generators': [6920176419218, 6227384421, 5167, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.HL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HL', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387647
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CC', '72.CG', '72.DQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1865, -1, 3262, -1], 'generators': [5167, 4097506695141, 1313941668480, 11536, 8396027160338, 4103734078087, 4103734078096], 'label': '18432.q.144.HM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HM', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387648
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CB', '72.CF', '72.DP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1003, -1, 2757, -1], 'generators': [6227384421, 5167, 1313941668480, 9709928549146, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.HN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HN', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387649
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CC', '72.CF', '72.DP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [984, -1, 3190, -1], 'generators': [5606275030426, 5167, 4097506695141, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.HO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HO', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387650
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CC', '72.CL', '72.CX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2140, -1, 3485, -1], 'generators': [16703, 4103734078080, 9709928564378, 40279703, 40279680, 1313941668480, 6354044781], 'label': '18432.q.144.HP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HP', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387651
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CB', '72.CM', '72.CX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2003, -1, 3394, -1], 'generators': [16703, 4103734078080, 40279703, 40279680, 9709928558626, 1313941668480, 6354039013], 'label': '18432.q.144.HQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HQ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387652
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CC', '72.CL', '72.CZ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2159, -1, 3575, -1], 'generators': [16703, 4103734078080, 5606321857197, 40279703, 40279680, 1313941668480, 6354044781], 'label': '18432.q.144.HR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HR', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387653
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '12.E', '12.F', '12.J'], 'contains': ['72.A', '96.G', '96.P', '96.W', '96.X', '96.BX', '96.BY', '96.CC', '96.CD', '96.CE', '96.CF', '96.CG'], 'core': '72.A', 'coset_action_label': None, 'count': 2, 'diagramx': [4998, -1, 4447, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 93409309459, 5167, 1313941668480, 11536, 7], 'label': '18432.q.24.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '24.s1', 'projective_image': '18432.q', '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': None}
  • id: 63387654
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CB', '72.CM', '72.CZ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1983, -1, 3412, -1], 'generators': [16703, 4103734078080, 5606321851429, 40279703, 40279680, 1313941668480, 6354039013], 'label': '18432.q.144.HS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HS', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387655
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CB', '72.CL', '72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2063, -1, 3172, -1], 'generators': [6227384421, 40284856, 5167, 9709928558626, 1313941668480, 11536, 40284847], 'label': '18432.q.144.HT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ho1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HT', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387656
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.HU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CC', '72.CM', '72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2101, -1, 3777, -1], 'generators': [40284856, 5167, 9709928558626, 4097506695141, 1313941668480, 11536, 40284847], 'label': '18432.q.144.HU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387657
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CB', '72.CL', '72.DB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2082, -1, 3015, -1], 'generators': [6227384421, 40284856, 5167, 1313941668480, 9709928549146, 11536, 40284847], 'label': '18432.q.144.HV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HV', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387658
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CC', '72.CM', '72.DB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2120, -1, 3593, -1], 'generators': [40284856, 5606275030426, 5167, 4097506695141, 1313941668480, 11536, 40284847], 'label': '18432.q.144.HW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HW', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387659
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CB', '72.CC', '72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2225, -1, 2694, -1], 'generators': [5606321841949, 5167, 2789792409600, 11536, 4103734078087, 4103646998400, 4103734078096], 'label': '18432.q.144.HX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.hs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HX', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387660
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CB', '72.CC', '72.DS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2250, -1, 2736, -1], 'generators': [87102727, 1313941668480, 87102736, 127387560, 16703, 4103734078080, 5606321851429], 'label': '18432.q.144.HY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ht1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387661
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2752, -1, 3878, -1], 'generators': [40284840, 16703, 4103734078080, 6227384421, 16, 1313941668480, 7], 'label': '18432.q.144.HZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DT', 'old_label': '144.hu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.HZ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387662
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CB', '72.CH', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2730, -1, 3966, -1], 'generators': [6227384421, 4103693803560, 5167, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.IA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.hv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IA', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387663
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CC', '72.CI', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2774, -1, 3948, -1], 'generators': [4103693803560, 5167, 4097506695141, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.IB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.hw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IB', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387664
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.A'], 'contains': ['48.BP', '48.BQ', '48.BR', '72.EC', '96.BZ', '96.CH', '96.CI'], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5170, -1, 4827, -1], 'generators': [4103734078080, 6227384421, 127387576, 87102720, 93409309459, 19615115146917, 5167, 1313941668480, 11536], 'label': '18432.q.24.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.T', 'old_label': '24.t1', 'projective_image': '18432.q', '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': '768.1090070'}
  • id: 63387665
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CH', '72.CI', '72.DW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4405, -1, 5088, -1], 'generators': [4097380065261, 4103693803560, 5167, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.IC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.hx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IC', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387666
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.ID', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CH', '72.CP', '72.DL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4808, -1, 5492, -1], 'generators': [6227384421, 127387576, 87102720, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.144.ID', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.hy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ID', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387667
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CI', '72.CQ', '72.DL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4451, -1, 5377, -1], 'generators': [127387576, 87102720, 5167, 4097506695141, 1313941668480, 11536, 127387567], 'label': '18432.q.144.IE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.hz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IE', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387668
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CH', '72.CQ', '72.DO'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4387, -1, 5243, -1], 'generators': [127387576, 87102720, 4097506695130, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.144.IF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.ia1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IF', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387669
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CI', '72.CP', '72.DO'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4347, -1, 5049, -1], 'generators': [6227384410, 127387576, 87102720, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.144.IG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.ib1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IG', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387670
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CD', '72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7771, -1, 8582, -1], 'generators': [4103693803567, 6227384421, 40284856, 5606275039906, 5167, 1313941668480, 11536], 'label': '18432.q.144.IH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.ic1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IH', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387671
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.CD', '72.CE', '72.CY'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7694, -1, 8702, -1], 'generators': [16703, 4103734078080, 5606321847717, 40279703, 1313941668480, 40284847, 6354044770], 'label': '18432.q.144.II', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.id1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.II', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387672
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CE', '72.CY'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5684, -1, 8471, -1], 'generators': [4103693803567, 40284856, 5606321841949, 5167, 1313941668480, 11536, 6354044770], 'label': '18432.q.144.IJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.ie1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IJ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387673
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CE', '72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7650, -1, 8506, -1], 'generators': [4103693803567, 6227384421, 40284856, 5167, 9709928558626, 1313941668480, 11536], 'label': '18432.q.144.IK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.if1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IK', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387674
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IL', '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': ['72.CD', '72.CE', '72.DC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7905, -1, 8720, -1], 'generators': [4103693803567, 6227384421, 40284856, 5167, 9709881737629, 1313941668480, 11536], 'label': '18432.q.144.IL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.ig1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IL', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387675
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.A'], 'contains': ['48.BV', '48.BW', '48.BX', '72.EG', '96.CI', '96.CJ', '96.CK'], 'core': '18432.a1', 'coset_action_label': '24T12470', 'count': 48, 'diagramx': [5225, -1, 4691, -1], 'generators': [6227384421, 5160, 11520, 93409305135, 4103734083247, 87102720, 127387560, 2789792421136, 19615115146917], 'label': '18432.q.24.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.U', 'old_label': '24.u1', 'projective_image': '18432.q', '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': '768.1090070'}
  • id: 63387676
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CD', '72.CY'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5703, -1, 8546, -1], 'generators': [4103693803567, 40284856, 5167, 9709881737629, 1313941668480, 11536, 6354044770], 'label': '18432.q.144.IM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.ih1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IM', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387677
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IN', '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': ['72.CD', '72.CE', '72.DK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7716, -1, 8657, -1], 'generators': [5606321841949, 5167, 1313941668480, 11536, 4103646998400, 4103606723896, 127387567], 'label': '18432.q.144.IN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.ii1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IN', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387678
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IO', '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': ['72.CE', '72.CJ', '72.DK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4171, -1, 4829, -1], 'generators': [16703, 87107887, 127382400, 127387576, 1313941668480, 4103734078080, 5606321847717], 'label': '18432.q.144.IO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.ij1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IO', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387679
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IP', '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': ['72.CD', '72.CE', '72.DL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7927, -1, 8681, -1], 'generators': [127387576, 87102720, 5167, 4097506695141, 1313941668480, 11536, 4103606723887], 'label': '18432.q.144.IP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.R', 'old_label': '144.ik1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IP', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387680
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IQ', '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': ['72.CD', '72.CK', '72.DK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4155, -1, 4868, -1], 'generators': [16703, 1313941668480, 87107887, 127382400, 127387576, 4103734078080, 5606321841949], 'label': '18432.q.144.IQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.il1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IQ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387681
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IR', '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': ['72.CJ', '72.CK', '72.DM'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3140, -1, 842, -1], 'generators': [16703, 1313941668480, 87107887, 127382400, 127387576, 4103734078080, 5606321857197], 'label': '18432.q.144.IR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.im1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IR', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387682
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CJ', '72.CR', '72.DK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3112, -1, 601, -1], 'generators': [16703, 1313941668480, 127382400, 87102720, 127387576, 4103734078080, 5606321841949], 'label': '18432.q.144.IS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.in1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IS', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387683
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CK', '72.CS', '72.DK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2969, -1, 868, -1], 'generators': [16703, 127382400, 87102720, 127387576, 1313941668480, 4103734078080, 5606321847717], 'label': '18432.q.144.IT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.io1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IT', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387684
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CK', '72.CR', '72.DM'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2953, -1, 826, -1], 'generators': [16703, 1313941668480, 127382400, 87102720, 127387576, 4103734078080, 5606321857197], 'label': '18432.q.144.IU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.ip1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IU', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387685
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CJ', '72.CS', '72.DM'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3096, -1, 757, -1], 'generators': [16703, 1313941668480, 127382400, 87102720, 127387576, 4103734078080, 5606321851429], 'label': '18432.q.144.IV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.iq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IV', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387686
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.B'], 'contains': ['64.B', '64.C', '64.D', '96.J', '96.K', '128.D'], 'core': '18432.a1', 'coset_action_label': '32T1119768', 'count': 32, 'diagramx': [3146, -1, 321, -1], 'generators': [5606234750738, 6227384421, 16, 93409310300, 5167, 11536, 843, 7], 'label': '18432.q.32.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.A', 'old_label': '32.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.A', 'subgroup_fusion': None, 'weyl_group': '576.5126'}
  • id: 63387687
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CG', '72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1349, -1, 2850, -1], 'generators': [87102720, 5167, 9709881737629, 2789792409600, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.IW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ir1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387688
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CJ', '72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2845, -1, 1715, -1], 'generators': [16703, 4103734078080, 16, 87102720, 5606321841949, 1313941668480, 5160], 'label': '18432.q.144.IX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.is1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IX', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387689
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CG', '72.CJ', '72.DS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2386, -1, 2307, -1], 'generators': [87102727, 87107903, 1313941668480, 127387560, 16703, 4103734078080, 5606321857197], 'label': '18432.q.144.IY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.it1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IY', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387690
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.IZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CG', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1527, -1, 3738, -1], 'generators': [40284840, 5167, 4097506695141, 1313941668480, 11536, 4103734078087, 4103734078096], 'label': '18432.q.144.IZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.iu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.IZ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387691
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CK', '72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2826, -1, 1754, -1], 'generators': [16703, 5160, 1313941668480, 87102720, 16, 4103734078080, 5606321847717], 'label': '18432.q.144.JA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.iv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JA', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387692
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CK', '72.DS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2370, -1, 2346, -1], 'generators': [87102727, 16703, 4103734078080, 127387560, 5606321851429, 1313941668480, 87107903], 'label': '18432.q.144.JB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.iw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JB', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387693
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CJ', '72.CK', '72.DU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2985, -1, 793, -1], 'generators': [16703, 4103734078080, 127387560, 87102736, 5606321841949, 1313941668480, 87107880], 'label': '18432.q.144.JC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.ix1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JC', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387694
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JD', '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': ['72.CJ', '72.CK', '72.DV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2937, -1, 778, -1], 'generators': [16703, 4103734078080, 16, 87102720, 9709928554898, 1313941668480, 5160], 'label': '18432.q.144.JD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.iy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JD', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387695
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CN', '72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1288, -1, 3304, -1], 'generators': [4103693803567, 6227384421, 4103693803576, 5606275039906, 5167, 1313941668480, 11536], 'label': '18432.q.144.JE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.iz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JE', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387696
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CG', '72.CN', '72.CZ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1308, -1, 3629, -1], 'generators': [16703, 4103734078080, 40284856, 5606321851429, 40279680, 1313941668480, 6354044781], 'label': '18432.q.144.JF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ja1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387697
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '16.A'], 'contains': ['96.N', '96.O', '96.P', '128.B', '128.C', '128.F', '128.H', '128.I'], 'core': '18432.a1', 'coset_action_label': '32T1119847', 'count': 16, 'diagramx': [3931, -1, 2006, -1], 'generators': [127387560, 16, 87102720, 93409310300, 5167, 11536, 843, 7], 'label': '18432.q.32.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.A', 'old_label': '32.b1', 'projective_image': '18432.q', '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': '1152.157861'}
  • id: 63387698
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CO', '72.CZ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1099, -1, 3052, -1], 'generators': [16703, 4103734078080, 5606321857197, 40284856, 40279680, 1313941668480, 6354044781], 'label': '18432.q.144.JG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JG', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387699
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CG', '72.CO', '72.CX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1390, -1, 3503, -1], 'generators': [16703, 4103734078080, 40284856, 40279680, 9709928558626, 1313941668480, 6354044781], 'label': '18432.q.144.JH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JH', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387700
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CG', '72.CO', '72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1371, -1, 3663, -1], 'generators': [4103693803567, 6227384421, 4103693803576, 5167, 9709928558626, 1313941668480, 11536], 'label': '18432.q.144.JI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JI', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387701
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CO', '72.DB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1080, -1, 3034, -1], 'generators': [4103693803567, 4103693803576, 5606275030426, 5167, 4097506695141, 1313941668480, 11536], 'label': '18432.q.144.JJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.je1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JJ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387702
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CG', '72.CN', '72.DB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1327, -1, 3539, -1], 'generators': [4103693803567, 4103693803576, 5167, 4097506695141, 1313941668480, 9709928549146, 11536], 'label': '18432.q.144.JK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JK', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387703
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CF', '72.CN', '72.CX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1200, -1, 2997, -1], 'generators': [16703, 4103734078080, 40284856, 9709928564378, 40279680, 1313941668480, 6354044781], 'label': '18432.q.144.JL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JL', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387704
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CH', '72.CP', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3949, -1, 4369, -1], 'generators': [40284840, 5160, 1313941668480, 5183, 6227384421, 16703, 4103734078080], 'label': '18432.q.144.JM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.jh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JM', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387705
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CI', '72.CQ', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3781, -1, 4916, -1], 'generators': [40284840, 5160, 1313941668480, 5183, 6227390173, 16703, 4103734078080], 'label': '18432.q.144.JN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.ji1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JN', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387706
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CI', '72.CP', '72.DW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3930, -1, 4423, -1], 'generators': [16703, 4103734078080, 16, 40279687, 1313941668480, 6354044781, 7], 'label': '18432.q.144.JO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.jj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JO', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387707
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CH', '72.CQ', '72.DW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3800, -1, 4973, -1], 'generators': [16703, 4103734078080, 16, 40279687, 1313941668480, 6354039013, 7], 'label': '18432.q.144.JP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.jk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JP', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387708
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '16.B'], 'contains': ['96.U', '96.V', '96.W', '128.A', '128.B', '128.F', '128.G'], 'core': '18432.a1', 'coset_action_label': '32T1119851', 'count': 16, 'diagramx': [3502, -1, 1287, -1], 'generators': [93409310300, 16, 7, 843, 1314028771200, 5167, 2789745614760, 11536], 'label': '18432.q.32.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '32.c1', 'projective_image': '18432.q', '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': '1152.155467'}
  • id: 63387709
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.A', '72.CH', '72.CI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4485, -1, 5103, -1], 'generators': [127387560, 87102720, 5167, 1313941668480, 11536, 4103734078096, 7], 'label': '18432.q.144.JQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.jl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JQ', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63387710
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CJ', '72.CR', '72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2655, -1, 524, -1], 'generators': [16703, 4103734078080, 87102720, 5606321841949, 5183, 1313941668480, 7], 'label': '18432.q.144.JR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.jm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JR', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387711
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CK', '72.CS', '72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2680, -1, 810, -1], 'generators': [16703, 7, 1313941668480, 5183, 87102720, 4103734078080, 5606321847717], 'label': '18432.q.144.JS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.jn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JS', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387712
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CK', '72.CR', '72.DV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2808, -1, 742, -1], 'generators': [16703, 4103734078080, 87102720, 9709928554898, 5183, 1313941668480, 7], 'label': '18432.q.144.JT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.jo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JT', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387713
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CJ', '72.CS', '72.DV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2874, -1, 687, -1], 'generators': [16703, 4103734078080, 87102720, 5183, 1313941668480, 9709928549146, 7], 'label': '18432.q.144.JU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.jp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JU', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387714
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.A', '72.CJ', '72.CK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3126, -1, 855, -1], 'generators': [127387560, 16, 87102720, 5167, 1313941668480, 11536, 4103734078087], 'label': '18432.q.144.JV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.jq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JV', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63387715
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.K', '72.CL', '72.CN', '72.DQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [803, -1, 2432, -1], 'generators': [6227384421, 16, 5167, 1313941668480, 11536, 8396027160338, 7], 'label': '18432.q.144.JW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JW', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387716
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.I', '72.CL', '72.CO', '72.DP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [616, -1, 2534, -1], 'generators': [6227384421, 16, 5167, 1313941668480, 9709928549146, 11536, 7], 'label': '18432.q.144.JX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.js1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JX', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387717
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.L', '72.CM', '72.CN', '72.DQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [654, -1, 2450, -1], 'generators': [6920176419218, 16, 5167, 4097506695141, 1313941668480, 11536, 7], 'label': '18432.q.144.JY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JY', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387718
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.JZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.J', '72.CM', '72.CO', '72.DP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [578, -1, 2492, -1], 'generators': [16, 5606275030426, 5167, 4097506695141, 1313941668480, 11536, 7], 'label': '18432.q.144.JZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ju1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.JZ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387719
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A'], 'contains': ['8.A', '12.E', '12.F', '64.F', '64.I', '64.K'], 'core': '8.A', 'coset_action_label': None, 'count': 2, 'diagramx': [5226, -1, 4568, -1], 'generators': [11536, 16, 843, 127387560, 4103734078080, 5167, 19615115146917, 7, 1313941668480, 87102720, 93409310300], 'label': '18432.q.4.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '4.b1', 'projective_image': '18432.q', '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': None}
  • id: 63387720
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.A', '16.C', '16.D', '16.E'], 'contains': ['96.BV', '96.BW', '96.BX', '128.A', '128.B', '128.C', '128.E'], 'core': '1152.A', 'coset_action_label': None, 'count': 8, 'diagramx': [3521, -1, 1399, -1], 'generators': [4103734078080, 16, 93409310300, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.32.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '32.d1', 'projective_image': '18432.q', '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': None}
  • id: 63387721
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.M', '72.CL', '72.CO', '72.DQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [751, -1, 2370, -1], 'generators': [6920176419218, 6227384421, 16, 5167, 1313941668480, 11536, 7], 'label': '18432.q.144.KA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KA', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387722
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.N', '72.CM', '72.CO', '72.DQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [674, -1, 2414, -1], 'generators': [16, 5167, 4097506695141, 1313941668480, 11536, 8396027160338, 7], 'label': '18432.q.144.KB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KB', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387723
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.O', '72.CL', '72.CN', '72.DP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [635, -1, 2552, -1], 'generators': [6227384421, 16, 5606275030426, 5167, 1313941668480, 11536, 7], 'label': '18432.q.144.KC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KC', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387724
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.P', '72.CM', '72.CN', '72.DP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [597, -1, 2593, -1], 'generators': [16, 5167, 4097506695141, 1313941668480, 9709928549146, 11536, 7], 'label': '18432.q.144.KD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KD', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387725
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.R', '72.CL', '72.CM', '72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [696, -1, 2471, -1], 'generators': [16, 87102720, 5606321841949, 5167, 2789792409600, 11536, 7], 'label': '18432.q.144.KE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.jz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KE', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387726
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Q', '72.CL', '72.CM', '72.DS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [720, -1, 2572, -1], 'generators': [16703, 4103734078080, 127387560, 5606321851429, 1313941668480, 87107903, 87107880], 'label': '18432.q.144.KF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '144.ka1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KF', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387727
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.S', '72.CL', '72.CP', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1256, -1, 3083, -1], 'generators': [40284840, 6227384421, 16, 5167, 1313941668480, 11536, 7], 'label': '18432.q.144.KG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.kb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KG', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387728
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.T', '72.CM', '72.CQ', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1218, -1, 3646, -1], 'generators': [40284840, 16, 5167, 4097506695141, 1313941668480, 11536, 7], 'label': '18432.q.144.KH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.kc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KH', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387729
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.U', '72.CP', '72.CQ', '72.DW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3758, -1, 4128, -1], 'generators': [40284840, 16, 5167, 1313941668480, 11536, 6354044781, 7], 'label': '18432.q.144.KI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BC', 'old_label': '144.kd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KI', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387730
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.W', '72.CN', '72.CO', '72.DR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [781, -1, 2326, -1], 'generators': [16, 5167, 9709881737629, 2789792409600, 11536, 4103646998400, 7], 'label': '18432.q.144.KJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ke1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KJ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387731
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A', '16.F'], 'contains': ['64.F', '64.H', '96.BZ'], 'core': '1152.A', 'coset_action_label': None, 'count': 16, 'diagramx': [4754, -1, 4620, -1], 'generators': [4103734078080, 6227384421, 93409310292, 19615115146917, 5167, 1313941668480, 860, 11536], 'label': '18432.q.32.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.e1', 'projective_image': '18432.q', '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': '1152.157849'}
  • id: 63387732
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.V', '72.CO', '72.CR', '72.DS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2045, -1, 1732, -1], 'generators': [87102727, 16703, 4103734078080, 5606321857197, 127382407, 1313941668480, 87107903], 'label': '18432.q.144.KK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '144.kf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KK', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 63387733
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.X', '72.CN', '72.CO', '72.DT'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [825, -1, 2513, -1], 'generators': [16, 4103693803560, 5167, 4097506695141, 1313941668480, 11536, 7], 'label': '18432.q.144.KL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.kg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KL', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387734
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Y', '72.CN', '72.CS', '72.DS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1882, -1, 1770, -1], 'generators': [87102727, 16703, 4103734078080, 5606321851429, 127382407, 1313941668480, 87107903], 'label': '18432.q.144.KM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '144.kh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KM', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 63387735
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.Z', '72.CR', '72.CS', '72.DU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2581, -1, 508, -1], 'generators': [87102727, 87107903, 1313941668480, 127382407, 16703, 4103734078080, 5606321841949], 'label': '18432.q.144.KN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '144.ki1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KN', 'subgroup_fusion': None, 'weyl_group': '96.228'}
  • id: 63387736
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BA', '72.A', '72.CP', '72.CQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3914, -1, 4354, -1], 'generators': [127387560, 16, 87102720, 5167, 1313941668480, 11536, 7], 'label': '18432.q.144.KO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '144.kj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KO', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63387737
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BB', '72.A', '72.CR', '72.CS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2639, -1, 700, -1], 'generators': [127387560, 16, 5167, 1313941668480, 11536, 4103646998400, 7], 'label': '18432.q.144.KP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '144.kk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KP', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63387738
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4217, -1, 4849, -1], 'generators': [87102720, 5167, 9709881737629, 1313941668480, 11536, 4103606723896, 127387567], 'label': '18432.q.144.KQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DK', 'old_label': '144.kl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KQ', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387739
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7538, -1, 8454, -1], 'generators': [6227384421, 4103693803576, 5167, 9709928558626, 1313941668480, 11536, 40284847], 'label': '18432.q.144.KR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DA', 'old_label': '144.km1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KR', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 63387740
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3276, -1, 4091, -1], 'generators': [4103693803576, 5606321841949, 5167, 1313941668480, 11536, 6354044781, 40284847], 'label': '18432.q.144.KS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DG', 'old_label': '144.kn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KS', 'subgroup_fusion': None, 'weyl_group': '64.56'}
  • id: 63387741
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CT', '72.CU', '72.DS'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1774, -1, 3283, -1], 'generators': [87102727, 4103734078080, 5606321847709, 40284856, 5167, 1313941668480, 11536], 'label': '18432.q.144.KT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ko1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KT', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387742
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.B', '16.F'], 'contains': ['64.G', '64.H', '96.CB', '128.D'], 'core': '1152.A', 'coset_action_label': None, 'count': 16, 'diagramx': [3768, -1, 1305, -1], 'generators': [4103734078080, 6266944090, 5167, 1313941668480, 11536, 93485161460, 8396027160338, 843], 'label': '18432.q.32.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.f1', 'projective_image': '18432.q', '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': '1152.157849'}
  • id: 63387743
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CU', '72.DK', '72.DR'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2563, -1, 3759, -1], 'generators': [4103734078080, 127387576, 5167, 1313941668480, 11536, 8396027160338, 127387567], 'label': '18432.q.144.KU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.kp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KU', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387744
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CT', '72.CU', '72.DT'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1903, -1, 3798, -1], 'generators': [23, 40284840, 4103734078080, 6227384421, 5167, 1313941668480, 11536], 'label': '18432.q.144.KV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.kq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KV', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387745
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CT', '72.DM', '72.DR'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2599, -1, 3358, -1], 'generators': [4103734078080, 127387576, 5167, 8396027166098, 1313941668480, 11536, 127387567], 'label': '18432.q.144.KW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.kr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KW', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387746
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DK', '72.DM', '72.DV'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [3834, -1, 3913, -1], 'generators': [4103734078080, 127387576, 5606321841949, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.144.KX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '144.ks1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KX', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387747
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CT', '72.DA', '72.DP'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1714, -1, 3681, -1], 'generators': [23, 4103734078080, 6227384421, 5167, 9709928558626, 1313941668480, 11536], 'label': '18432.q.144.KY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.kt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KY', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387748
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.KZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BD', '72.CT', '72.CX', '72.DQ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2178, -1, 2674, -1], 'generators': [23, 4103734078080, 6266944101, 5167, 1313941668480, 11536, 8396027169818], 'label': '18432.q.144.KZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ku1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.KZ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387749
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CU', '72.CX', '72.DP'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1593, -1, 3699, -1], 'generators': [23, 4103734078080, 6266944101, 5167, 1313941668480, 9709928549146, 11536], 'label': '18432.q.144.LA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.kv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LA', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387750
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BC', '72.CU', '72.CZ', '72.DQ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1944, -1, 2889, -1], 'generators': [23, 4103734078080, 6266944101, 5167, 1313941668480, 11536, 8396027160338], 'label': '18432.q.144.LB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.kw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LB', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387751
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BE', '72.CU', '72.DA', '72.DQ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1925, -1, 2871, -1], 'generators': [23, 4103734078080, 6227384421, 5167, 1313941668480, 11536, 8396027160338], 'label': '18432.q.144.LC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.kx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LC', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387752
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BF', '72.CT', '72.DB', '72.DQ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1963, -1, 2715, -1], 'generators': [23, 4103734078080, 6227384421, 5167, 1313941668480, 11536, 8396027169818], 'label': '18432.q.144.LD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.ky1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LD', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387753
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.C', '16.F'], 'contains': ['64.H'], 'core': '1152.A', 'coset_action_label': None, 'count': 16, 'diagramx': [4683, -1, 1870, -1], 'generators': [4103734078080, 6227384421, 11219048432047, 5167, 1313941668480, 860, 11536, 93528701291], 'label': '18432.q.32.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.F', 'old_label': '32.g1', 'projective_image': '18432.q', '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': '1152.157849'}
  • id: 63387754
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CU', '72.DB', '72.DP'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1574, -1, 3717, -1], 'generators': [23, 4103734078080, 6227384421, 5167, 1313941668480, 9709928549146, 11536], 'label': '18432.q.144.LE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.kz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LE', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387755
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CT', '72.CZ', '72.DP'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1733, -1, 3557, -1], 'generators': [23, 4103734078080, 6266944101, 5167, 9709928558626, 1313941668480, 11536], 'label': '18432.q.144.LF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.la1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387756
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CV', '72.CW', '72.DJ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8746, -1, 7849, -1], 'generators': [18301133924517, 4103734078080, 87102736, 5167, 1313941668480, 11536, 7], 'label': '18432.q.144.LG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.lb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LG', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387757
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CX', '72.CY', '72.CZ', '72.DA', '72.DK', '72.DR', '72.DS'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2908, -1, 3930, -1], 'generators': [87102727, 4103734078080, 5606321847709, 87102736, 5167, 1313941668480, 11536], 'label': '18432.q.144.LH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.lc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LH', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387758
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CV', '72.DA', '72.DB', '72.DC', '72.DD', '72.DL', '72.DT'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [8012, -1, 8437, -1], 'generators': [4103734078080, 6227384421, 40284856, 5167, 1313941668480, 11536, 40284847], 'label': '18432.q.144.LI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.ld1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LI', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 63387759
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CX', '72.DB', '72.DE', '72.DF', '72.DM', '72.DR', '72.DU'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3003, -1, 3819, -1], 'generators': [87102727, 4103734078080, 87102736, 5606321841949, 5167, 1313941668480, 11536], 'label': '18432.q.144.LJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.le1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LJ', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387760
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CZ', '72.DB', '72.DG', '72.DH', '72.DM', '72.DS', '72.DV'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2890, -1, 3835, -1], 'generators': [87102727, 4103734078080, 87102736, 9709928554906, 5167, 1313941668480, 11536], 'label': '18432.q.144.LK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.lf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LK', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387761
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CW', '72.CY', '72.DF', '72.DH', '72.DI', '72.DL', '72.DW'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [8070, -1, 7619, -1], 'generators': [4103734078080, 40284856, 5167, 1313941668480, 11536, 40284847, 6354044770], 'label': '18432.q.144.LL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.lg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LL', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 63387762
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CX', '72.CZ', '72.DE', '72.DG', '72.DO', '72.DT', '72.DW'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3295, -1, 4073, -1], 'generators': [4103734078080, 40284856, 5167, 1313941668480, 11536, 6354044781, 40284847], 'label': '18432.q.144.LM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.lh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LM', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387763
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CY', '72.DC', '72.DE', '72.DG', '72.DK', '72.DU', '72.DV'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3332, -1, 4149, -1], 'generators': [87102727, 4103734078080, 87102736, 5167, 1313941668480, 9709928549146, 11536], 'label': '18432.q.144.LN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.li1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LN', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387764
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.C'], 'contains': ['64.J'], 'core': '18432.a1', 'coset_action_label': '32T1119761', 'count': 32, 'diagramx': [4704, -1, 3988, -1], 'generators': [4103606723880, 6227384421, 6611, 2789705329920, 11520, 5160, 11219135529616, 93409319531], 'label': '18432.q.32.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.H', 'old_label': '32.h1', 'projective_image': '18432.q', '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': '576.8652'}
  • id: 63387765
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.A', '72.DJ', '72.DK', '72.DL', '72.DM', '72.DN', '72.DO'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [4420, -1, 5363, -1], 'generators': [4103734078080, 127387576, 87102720, 5167, 1313941668480, 11536, 7], 'label': '18432.q.144.LO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.lj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LO', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 63387766
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BG', '48.BI', '72.DP', '72.DQ', '72.DS'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2025, -1, 2225, -1], 'generators': [4103734078080, 5606321851429, 87102736, 5167, 1313941668480, 11536, 40284847], 'label': '18432.q.144.LP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.C', 'old_label': '144.lk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LP', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387767
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BH', '48.BJ', '72.DQ', '72.DR'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2281, -1, 575, -1], 'generators': [4103734078080, 16, 5167, 1313941668480, 11536, 8396027160338, 7], 'label': '18432.q.144.LQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '144.ll1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LQ', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 63387768
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BK', '48.BL', '48.BM', '72.DP', '72.DQ', '72.DT'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2344, -1, 2614, -1], 'generators': [4103734078080, 6227384421, 16, 5167, 1313941668480, 11536, 7], 'label': '18432.q.144.LR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '144.lm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LR', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387769
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BN', '72.DP', '72.DR', '72.DV'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2316, -1, 2396, -1], 'generators': [4103734078080, 16, 5606321841949, 5167, 1313941668480, 11536, 7], 'label': '18432.q.144.LS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '144.ln1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LS', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387770
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BO', '72.A', '72.DR', '72.DS', '72.DT', '72.DU', '72.DV', '72.DW'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2860, -1, 3157, -1], 'generators': [4103734078080, 16, 87102720, 5167, 1313941668480, 11536, 7], 'label': '18432.q.144.LT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '144.lo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LT', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63387771
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CV', '72.EB', '72.EC'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8590, -1, 8400, -1], 'generators': [18301133924517, 4103734078080, 87102743, 5167, 180591240257, 1313941668480, 11536], 'label': '18432.q.144.LU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.lp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387772
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CW', '72.EB', '72.EC'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8609, -1, 8001, -1], 'generators': [18301133924517, 4103734078080, 87102743, 180627523321, 5167, 1313941668480, 11536], 'label': '18432.q.144.LV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.lq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LV', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387773
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CV', '72.DX', '72.EC'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8944, -1, 8980, -1], 'generators': [4103734078080, 87102743, 180667070641, 5167, 1313941668480, 20835607967277, 11536], 'label': '18432.q.144.LW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.lr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LW', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387774
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CW', '72.DY', '72.EC'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8807, -1, 8074, -1], 'generators': [4103734078080, 87102743, 180703353737, 5167, 1313941668480, 20835607967277, 11536], 'label': '18432.q.144.LX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '144.ls1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LX', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387775
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A'], 'contains': ['64.K', '64.L', '96.CJ'], 'core': '18432.a1', 'coset_action_label': '32T1119762', 'count': 32, 'diagramx': [6087, -1, 4474, -1], 'generators': [2789705318416, 15860, 16, 1307714300762, 19615115146917, 2615428585451, 4103606707223, 7], 'label': '18432.q.32.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.I', 'old_label': '32.i1', 'projective_image': '18432.q', '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': '576.8654'}
  • id: 63387776
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DA', '72.DX', '72.DZ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [9368, -1, 9127, -1], 'generators': [4103734078080, 6227384421, 40284856, 5167, 1313941668480, 11536, 8396027160338], 'label': '18432.q.144.LY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.lt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LY', 'subgroup_fusion': None, 'weyl_group': '128.1578'}
  • id: 63387777
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.LZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CV', '72.DZ', '72.EB'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [9002, -1, 9034, -1], 'generators': [18301133924517, 4103734078080, 87102743, 180667070641, 5167, 1313941668480, 11536], 'label': '18432.q.144.LZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '144.lu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.LZ', 'subgroup_fusion': None, 'weyl_group': '256.16888'}
  • id: 63387778
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DD', '72.DX', '72.DZ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [9187, -1, 9194, -1], 'generators': [40284840, 4103734078080, 11219048432047, 6227383801, 5167, 1313941668480, 11536], 'label': '18432.q.144.MA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '144.lv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MA', 'subgroup_fusion': None, 'weyl_group': '128.1758'}
  • id: 63387779
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DH', '72.DY', '72.EA'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8906, -1, 8333, -1], 'generators': [4103734078080, 40284856, 5606321851429, 5167, 1313941668480, 6314485101, 11536], 'label': '18432.q.144.MB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.N', 'old_label': '144.lw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MB', 'subgroup_fusion': None, 'weyl_group': '128.236'}
  • id: 63387780
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.CW', '72.EA', '72.EB'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8845, -1, 8219, -1], 'generators': [18301133924517, 4103734078080, 87102743, 180703353737, 5167, 1313941668480, 11536], 'label': '18432.q.144.MC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '144.lx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MC', 'subgroup_fusion': None, 'weyl_group': '256.5675'}
  • id: 63387781
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DI', '72.DY', '72.EA'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8886, -1, 8419, -1], 'generators': [40284840, 4103734078080, 5167, 6314486521, 1313941668480, 11536, 11219135523247], 'label': '18432.q.144.MD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.N', 'old_label': '144.ly1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MD', 'subgroup_fusion': None, 'weyl_group': '128.859'}
  • id: 63387782
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.ME', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BQ', '72.DJ', '72.EB', '72.EC'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [6391, -1, 7580, -1], 'generators': [87102727, 4103734078080, 127387576, 19440678730917, 5167, 1313941668480, 11536], 'label': '18432.q.144.ME', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.lz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ME', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387783
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BP', '72.DJ', '72.EC'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6284, -1, 6385, -1], 'generators': [4103734078080, 87102743, 127387560, 16906281265317, 5167, 1313941668480, 11536], 'label': '18432.q.144.MF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '144.ma1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MF', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 63387784
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BR', '72.DL', '72.EB', '72.EC'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8188, -1, 7640, -1], 'generators': [4103734078080, 6227384421, 40284856, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.144.MG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.P', 'old_label': '144.mb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MG', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387785
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DJ', '72.DN', '72.EB'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6412, -1, 6517, -1], 'generators': [4103734078080, 87102743, 127387560, 20835531390117, 5167, 1313941668480, 11536], 'label': '18432.q.144.MH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.mc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MH', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387786
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.A', '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': ['18.E'], 'contains': ['72.N', '72.P', '72.Q', '72.BJ', '72.BK', '72.BR', '72.BS'], 'core': '18432.a1', 'coset_action_label': '36T11198', 'count': 36, 'diagramx': [6512, -1, 6933, -1], 'generators': [127387560, 87102720, 20835531390117, 4103734089616, 5167, 2789792409600, 3923142870961, 4103734078096, 7], 'label': '18432.q.36.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '36.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.A', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387787
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MI', 'aut_quo_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', '72.DX'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 72, 'diagramx': [9103, -1, 9054, -1], 'generators': [4103734078080, 87302043493, 5167, 1313941668480, 11536, 8396027160338, 13834520547263], 'label': '18432.q.144.MI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DX', 'old_label': '144.md1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MI', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387788
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.DX'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 72, 'diagramx': [9346, -1, 9078, -1], 'generators': [4103734078080, 87302043493, 5167, 1313941668480, 11536, 6920223230757, 13834520547263], 'label': '18432.q.144.MJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.DX', 'old_label': '144.me1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MJ', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387789
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MK', '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': ['72.B', '72.ED', '72.EE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7228, -1, 6749, -1], 'generators': [180591223822, 7, 87091216, 5183, 1313988485176, 2789792414767, 19440635179549], 'label': '18432.q.144.MK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MK', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387790
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.C', '72.ED', '72.EE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7305, -1, 6804, -1], 'generators': [1313988485176, 7, 1401123605041, 87091216, 5183, 2789792414767, 20835531384349], 'label': '18432.q.144.ML', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ML', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387791
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.B', '72.EE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7209, -1, 6612, -1], 'generators': [180591228737, 1313988485176, 5183, 87091216, 20835531384349, 7, 2789792414767], 'label': '18432.q.144.MM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MM', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387792
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.C', '72.EE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7247, -1, 6630, -1], 'generators': [1401123600126, 1313988485176, 5183, 87091216, 20835531384349, 7, 2789792414767], 'label': '18432.q.144.MN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MN', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387793
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.B', '72.ED'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7121, -1, 6785, -1], 'generators': [180591228737, 19440635179549, 1313988485176, 5183, 87091216, 7, 2789792414767], 'label': '18432.q.144.MO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MO', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387794
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.C', '72.ED'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7140, -1, 6858, -1], 'generators': [1401123600126, 19440635179549, 1313988485176, 5183, 87091216, 7, 2789792414767], 'label': '18432.q.144.MP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MP', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387795
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.D'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5386, -1, 7364, -1], 'generators': [1313988485176, 1307714284937, 1313941668496, 11219135523247, 87091216, 7, 1313941673647], 'label': '18432.q.144.MQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.D', 'old_label': '144.ml1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MQ', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 63387796
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.E'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5515, -1, 7459, -1], 'generators': [4103606723880, 2789705329920, 1313941673647, 1313941668487, 11219135523247, 4097506694537, 1313941680000], 'label': '18432.q.144.MR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.E', 'old_label': '144.mm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MR', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 63387797
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.E'], 'contains': ['72.B', '72.C', '72.F', '72.G', '72.N', '72.O', '72.BK', '72.BL', '72.BO', '72.ED', '72.EE', '72.EF', '72.EG'], 'core': '18432.a1', 'coset_action_label': '36T11196', 'count': 18, 'diagramx': [7174, -1, 6885, -1], 'generators': [127387560, 87102720, 20835531390117, 4103734089616, 180591240241, 5167, 2789792409600, 4103734078096, 7], 'label': '18432.q.36.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '36.b1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.B', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387798
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.H'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5490, -1, 7418, -1], 'generators': [2796019793417, 2789745614760, 1313941668487, 2789792409616, 11219135529616, 4103646998400, 1313941673647], 'label': '18432.q.144.MS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.H', 'old_label': '144.mn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MS', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 63387799
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.I'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5589, -1, 7559, -1], 'generators': [2789792421120, 1314028759696, 6227383817, 127376056, 11219135529616, 7, 1313941673647], 'label': '18432.q.144.MT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.I', 'old_label': '144.mo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MT', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 63387800
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.F', '72.EE', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7044, -1, 6912, -1], 'generators': [1313941680000, 7, 1313988485176, 1401123600126, 1314028776367, 2789792414767, 20835531384349], 'label': '18432.q.144.MU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MU', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387801
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.F', '72.ED', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6802, -1, 6930, -1], 'generators': [1313941680000, 7, 1313988485176, 1401123600126, 1314028776367, 2789792414767, 19440635179549], 'label': '18432.q.144.MV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MV', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387802
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MW', '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': ['72.G', '72.EE', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7344, -1, 6948, -1], 'generators': [1313941680000, 7, 1313988485176, 180591228737, 1314028776367, 2789792414767, 20835531384349], 'label': '18432.q.144.MW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MW', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387803
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MX', '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': ['72.G', '72.ED', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7266, -1, 6966, -1], 'generators': [1313941680000, 7, 1313988485176, 180591228737, 1314028776367, 2789792414767, 19440635179549], 'label': '18432.q.144.MX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.ms1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MX', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387804
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.F', '72.EE', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6840, -1, 6767, -1], 'generators': [1313941680000, 7, 1401123605041, 1314028776367, 1313988485176, 2789792414767, 19440635179549], 'label': '18432.q.144.MY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MY', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387805
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.MZ', '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': ['72.G', '72.EE', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7363, -1, 6822, -1], 'generators': [1313941680000, 7, 180591223822, 1314028776367, 1313988485176, 2789792414767, 19440635179549], 'label': '18432.q.144.MZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.MZ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387806
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NA', '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': ['72.F', '72.ED', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7082, -1, 7039, -1], 'generators': [1314028776367, 1401123605041, 2789792414767, 20835531384349, 1313941680000, 7, 1313988485176], 'label': '18432.q.144.NA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NA', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387807
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.G', '72.ED', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7325, -1, 7093, -1], 'generators': [1313941680000, 7, 180591223822, 1314028776367, 1313988485176, 2789792414767, 20835531384349], 'label': '18432.q.144.NB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NB', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387808
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.E'], 'contains': ['72.O', '72.P', '72.BO', '72.BP', '72.BR'], 'core': '18432.a1', 'coset_action_label': '36T11197', 'count': 18, 'diagramx': [6861, -1, 6962, -1], 'generators': [127387560, 7, 4103734078096, 180591240241, 87102720, 5167, 4103734089616, 2789792409600, 20835531393818], 'label': '18432.q.36.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '36.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.C', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387809
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.D'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5414, -1, 7337, -1], 'generators': [4103606723880, 1307714296441, 1313941668487, 2789705329920, 11520, 11219135529616, 1313941673647], 'label': '18432.q.144.NC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.D', 'old_label': '144.mx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NC', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 63387810
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.ND', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.E'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5535, -1, 7479, -1], 'generators': [16, 1313988485176, 4097506706041, 11219135529616, 87091216, 7, 1313941673647], 'label': '18432.q.144.ND', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.E', 'old_label': '144.my1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ND', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 63387811
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NE', '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': ['72.B', '72.EF', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6909, -1, 6576, -1], 'generators': [127387560, 87102720, 180591240241, 11520, 19440635185317, 5160, 2789792414767], 'label': '18432.q.144.NE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.mz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NE', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387812
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NF', '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': ['72.C', '72.EF', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6928, -1, 6594, -1], 'generators': [127387560, 87102720, 20835531390117, 1401123588622, 11520, 5160, 2789792414767], 'label': '18432.q.144.NF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.na1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NF', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387813
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.B', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6670, -1, 6424, -1], 'generators': [127387560, 87102720, 20835531390117, 11520, 180591235326, 5160, 2789792414767], 'label': '18432.q.144.NG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.nb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NG', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387814
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.C', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6698, -1, 6558, -1], 'generators': [127387560, 87102720, 20835531390117, 1401123593537, 11520, 5160, 2789792414767], 'label': '18432.q.144.NH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.nc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NH', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387815
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.B', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7006, -1, 6713, -1], 'generators': [127387560, 87102720, 11520, 19440635185317, 180591235326, 5160, 2789792414767], 'label': '18432.q.144.NI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.nd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NI', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387816
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.C', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7025, -1, 6731, -1], 'generators': [127387560, 87102720, 1401123593537, 11520, 19440635185317, 5160, 2789792414767], 'label': '18432.q.144.NJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.ne1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NJ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387817
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NK', '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': ['72.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9936, -1, 9912, -1], 'generators': [6920263510429, 1313941673656, 127387560, 87096383, 15229253088000, 1482078135010, 4103734094783], 'label': '18432.q.144.NK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.J', 'old_label': '144.nf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NK', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387818
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NL', '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': ['72.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9995, -1, 9967, -1], 'generators': [1313941673656, 127387560, 87096383, 5606321841949, 87181920741, 4103734094783, 15229253093167], 'label': '18432.q.144.NL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.J', 'old_label': '144.nf2', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NL', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387819
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.G'], 'contains': ['72.D', '72.H', '72.R', '72.BY', '72.CA'], 'core': '18432.a1', 'coset_action_label': '36T11203', 'count': 18, 'diagramx': [5842, -1, 7437, -1], 'generators': [4103606723880, 16, 4103734089616, 5167, 1313941668480, 6227383817, 11219135523247, 4103646998400, 7], 'label': '18432.q.36.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '36.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.D', 'subgroup_fusion': None, 'weyl_group': '256.1529'}
  • id: 63387820
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9911, -1, 9991, -1], 'generators': [1313941673656, 127387560, 87102720, 5606321841949, 87181920741, 4103734094783, 11300123081647], 'label': '18432.q.144.NM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.J', 'old_label': '144.ng1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NM', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387821
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NN', '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': ['72.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [9966, -1, 9939, -1], 'generators': [1314028776367, 127387560, 1482078131293, 5606321851418, 15229253088000, 4103734094783, 1313941680007], 'label': '18432.q.144.NN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.J', 'old_label': '144.nh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NN', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 63387822
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.N'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [6203, -1, 6066, -1], 'generators': [127387560, 16, 20835531390117, 4103734083247, 5160, 87091216, 1313941680016], 'label': '18432.q.144.NO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.N', 'old_label': '144.ni1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NO', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387823
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.O'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [6565, -1, 5893, -1], 'generators': [127370903, 6227384421, 87096383, 4103734089616, 11520, 5160, 2789792414767], 'label': '18432.q.144.NP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.O', 'old_label': '144.nj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NP', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387824
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.N', '72.Z'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5998, -1, 5836, -1], 'generators': [127387560, 2789792414767, 7, 16687, 87102720, 1313941680016, 20835531390117], 'label': '18432.q.144.NQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.nk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NQ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387825
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.N', '72.P', '72.BA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6062, -1, 5928, -1], 'generators': [127387560, 2789792414767, 7, 16687, 87102720, 1313941680016, 16906314287397], 'label': '18432.q.144.NR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.nl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NR', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387826
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.P', '72.Z'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5980, -1, 5820, -1], 'generators': [127387560, 2789792414767, 7, 16687, 87102720, 1313941680016, 18301210492197], 'label': '18432.q.144.NS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.nm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NS', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387827
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NT', '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': ['72.R'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5260, -1, 6196, -1], 'generators': [127370903, 6227384421, 16696, 4103734089616, 87107887, 16687, 2789792414767], 'label': '18432.q.144.NT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.R', 'old_label': '144.nn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NT', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387828
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.Z'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5794, -1, 5663, -1], 'generators': [87096383, 4103734083247, 5183, 19440635185317, 5160, 127376056, 1313941680016], 'label': '18432.q.144.NU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.Z', 'old_label': '144.no1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NU', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387829
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.NV', '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': ['72.Z'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [5844, -1, 5710, -1], 'generators': [127387560, 87102720, 20835531390117, 4103734083247, 5183, 7, 1313941680016], 'label': '18432.q.144.NV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.Z', 'old_label': '144.np1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NV', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387830
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.B'], 'contains': ['8.A', '12.G', '12.H', '16.B', '16.C', '16.D'], 'core': '8.A', 'coset_action_label': None, 'count': 2, 'diagramx': [3128, -1, 1308, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 93409310300, 5606321841949, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.4.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '4.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.C', 'subgroup_fusion': None, 'weyl_group': '2880.eg'}
  • id: 63387831
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.G'], 'contains': ['72.E', '72.I', '72.R', '72.BZ', '72.CA'], 'core': '18432.a1', 'coset_action_label': '36T11204', 'count': 18, 'diagramx': [6079, -1, 7492, -1], 'generators': [4103606723880, 16, 4103734089616, 5167, 1313941668480, 6227383817, 11219135529616, 4103646998400, 7], 'label': '18432.q.36.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '36.e1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.E', 'subgroup_fusion': None, 'weyl_group': '256.1529'}
  • id: 63387832
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.N', '72.ED', '72.EE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7162, -1, 6674, -1], 'generators': [127387560, 16696, 20835531390117, 4103734083247, 11520, 87091216, 1313941680016], 'label': '18432.q.144.NW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.nq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NW', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387833
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.N', '72.Z', '72.EE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6181, -1, 6110, -1], 'generators': [127387560, 87102720, 20835531390117, 11543, 5183, 2789792414767, 1313941680016], 'label': '18432.q.144.NX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.nr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NX', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387834
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.O', '72.ED', '72.EE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7187, -1, 6651, -1], 'generators': [6227384421, 16696, 87096383, 4103734089616, 127376056, 16687, 2789792414767], 'label': '18432.q.144.NY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.ns1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NY', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387835
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.P', '72.Z', '72.BA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5948, -1, 5778, -1], 'generators': [127387560, 87102720, 18301210492197, 11543, 5183, 2789792414767, 1313941680016], 'label': '18432.q.144.NZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.nt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.NZ', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387836
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.N', '72.BA', '72.ED'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6162, -1, 6312, -1], 'generators': [127387560, 87102720, 11543, 5183, 16906314287397, 2789792414767, 1313941680016], 'label': '18432.q.144.OA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.nu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OA', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387837
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.OB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.R'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5285, -1, 6173, -1], 'generators': [6227384421, 127382407, 4103734089616, 11543, 5183, 87107887, 2789792414767], 'label': '18432.q.144.OB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.R', 'old_label': '144.nv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OB', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387838
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['48.BT', '72.Z'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5758, -1, 5172, -1], 'generators': [127387560, 87102720, 20835531390117, 4103734083247, 11543, 16687, 1313941680016], 'label': '18432.q.144.OC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.Z', 'old_label': '144.nw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OC', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387839
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['48.BS', '72.Z'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5650, -1, 5134, -1], 'generators': [127387560, 18301210492197, 11543, 87091216, 16687, 2789792414767, 1313941680016], 'label': '18432.q.144.OD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '144.nx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OD', 'subgroup_fusion': None, 'weyl_group': '96.229'}
  • id: 63387840
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.Z', '72.BA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5915, -1, 5729, -1], 'generators': [127387560, 11543, 16906314287397, 87091216, 16687, 2789792414767, 1313941680016], 'label': '18432.q.144.OE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BA', 'old_label': '144.ny1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OE', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 63387841
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [8166, -1, 7601, -1], 'generators': [87096367, 2789792414767, 7, 127382407, 180591223806, 1313941680016, 19440711752997], 'label': '18432.q.144.OF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.BL', 'old_label': '144.nz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OF', 'subgroup_fusion': None, 'weyl_group': '64.267'}
  • id: 63387842
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.A'], 'contains': ['72.J', '72.K', '72.BB', '72.BC', '72.BD', '72.BE', '72.BL', '72.BM', '72.BQ'], 'core': '18432.a1', 'coset_action_label': '36T11659', 'count': 18, 'diagramx': [9552, -1, 9558, -1], 'generators': [23, 4103734078080, 127387560, 87102720, 5606321841949, 87181920741, 11300123081647, 1313941673647, 1313941680016], 'label': '18432.q.36.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.f1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.F', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387843
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [6481, -1, 7284, -1], 'generators': [87096367, 7, 180591223822, 127387560, 2789792414767, 4103734089616, 20835531390117], 'label': '18432.q.144.OG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.BR', 'old_label': '144.oa1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OG', 'subgroup_fusion': None, 'weyl_group': '64.56'}
  • id: 63387844
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BL', '72.ED', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7421, -1, 7266, -1], 'generators': [127387560, 180591223806, 5160, 87091200, 19440711752997, 2789792414767, 1313941680016], 'label': '18432.q.144.OH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.ob1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OH', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387845
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BK', '72.EE', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7063, -1, 6876, -1], 'generators': [127387560, 180591240241, 19440635185317, 5160, 87091200, 2789792414767, 1313941680016], 'label': '18432.q.144.OI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.oc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OI', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387846
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BK', '72.ED', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6717, -1, 6894, -1], 'generators': [87096367, 2789792414767, 7, 180591223822, 127387560, 1313941680016, 16906314287397], 'label': '18432.q.144.OJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.od1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OJ', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387847
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BK', '72.EE', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6736, -1, 6695, -1], 'generators': [127387560, 20835531390117, 4103734089616, 180591235326, 5160, 87091200, 2789792414767], 'label': '18432.q.144.OK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.oe1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OK', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387848
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['72.BL', '72.EE', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7382, -1, 6840, -1], 'generators': [127387560, 180591223806, 20835607957797, 5160, 87091200, 2789792414767, 1313941680016], 'label': '18432.q.144.OL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.of1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OL', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387849
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.OM', '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': ['72.BO', '72.EE', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7440, -1, 6985, -1], 'generators': [127387560, 180591223806, 19440635185317, 5160, 87091200, 2789792414767, 1313941680016], 'label': '18432.q.144.OM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.og1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OM', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387850
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.ON', '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': ['72.BO', '72.ED', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7285, -1, 7003, -1], 'generators': [87096367, 2789792414767, 7, 180591223806, 127387560, 1313941680016, 16906314287397], 'label': '18432.q.144.ON', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.oh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ON', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387851
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.OO', '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': ['72.BK', '72.ED', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7101, -1, 7021, -1], 'generators': [180591228737, 2789792414767, 7, 127382407, 87096367, 4103734089616, 18301210492197], 'label': '18432.q.144.OO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.oi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OO', 'subgroup_fusion': None, 'weyl_group': '128.2163'}
  • id: 63387852
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.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': ['48.BU', '72.R'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5177, -1, 5335, -1], 'generators': [6227384421, 4103734089616, 11520, 87107887, 5160, 127376056, 2789792414767], 'label': '18432.q.144.OP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.R', 'old_label': '144.oj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OP', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 63387853
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.A'], 'contains': ['72.BF', '72.BG', '72.BH', '72.BI', '72.BM', '72.BP', '72.BQ'], 'core': '18432.a1', 'coset_action_label': '36T11666', 'count': 18, 'diagramx': [9322, -1, 9433, -1], 'generators': [23, 1313941680016, 1313941673647, 11300123081647, 87181920741, 87102720, 127387560, 4103734078080, 5606321847717], 'label': '18432.q.36.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.g1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.G', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387854
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.OQ', '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': ['48.BW', '72.N', '72.EF', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6228, -1, 6131, -1], 'generators': [16, 4103734083247, 87107887, 19440635185317, 127376056, 7, 1313941680016], 'label': '18432.q.144.OQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.ok1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OQ', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387855
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.OR', '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': ['48.BV', '72.N', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5666, -1, 5943, -1], 'generators': [127387560, 2789792414767, 7, 87096383, 16, 1313941680016, 16906314287397], 'label': '18432.q.144.OR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '144.ol1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OR', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 63387856
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.OS', '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': ['48.BX', '72.O', '72.EF', '72.EG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6366, -1, 5963, -1], 'generators': [6227384421, 2789792414767, 7, 127382407, 87096383, 16, 4103734089616], 'label': '18432.q.144.OS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.B', 'old_label': '144.om1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OS', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 63387857
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '144.OT', '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': ['72.N', '72.P', '72.EF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6251, -1, 6330, -1], 'generators': [127387560, 87102720, 18301210492197, 11520, 5160, 2789792414767, 1313941680016], 'label': '18432.q.144.OT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '144.on1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.OT', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 63387858
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.X', '96.E'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1294, -1, 1817, -1], 'generators': [6227384421, 16, 4103693798407, 1313941668480, 843, 7], 'label': '18432.q.192.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.E', 'old_label': '192.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.A', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387859
    {'ambient': '18432.q', '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': ['48.BA', '96.A', '96.B', '96.N'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3700, -1, 2040, -1], 'generators': [127387560, 87102720, 11520, 1313941668480, 5160, 843], 'label': '18432.q.192.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '192.b1', 'projective_image': '18432.q', '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': '24.12'}
  • id: 63387860
    {'ambient': '18432.q', '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': 1, 'contained_in': ['48.BA', '96.C', '96.D', '96.N'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3662, -1, 2083, -1], 'generators': [127370903, 16, 1313941668480, 87091216, 843, 7], 'label': '18432.q.192.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '192.c1', 'projective_image': '18432.q', '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': '24.12'}
  • id: 63387861
    {'ambient': '18432.q', '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': ['48.R', '96.H'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [524, -1, 395, -1], 'generators': [6611, 11543, 5606321851418, 87107887, 2789792409600, 16687], 'label': '18432.q.192.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.H', 'old_label': '192.d1', 'projective_image': '18432.q', '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': '48.48'}
  • id: 63387862
    {'ambient': '18432.q', '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': ['48.BB', '96.N'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3601, -1, 1771, -1], 'generators': [127370903, 16, 4103646986896, 1313941668480, 843, 7], 'label': '18432.q.192.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.N', 'old_label': '192.e1', 'projective_image': '18432.q', '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': '12.3'}
  • id: 63387863
    {'ambient': '18432.q', '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': 1, 'contained_in': ['48.BA', '96.U'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3384, -1, 1537, -1], 'generators': [11543, 87107887, 1313941668480, 127376056, 843, 16687], 'label': '18432.q.192.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.U', 'old_label': '192.f1', 'projective_image': '18432.q', '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': '12.3'}
  • id: 63387864
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.C'], 'contains': ['72.L', '72.M', '72.BN', '72.BS', '72.BT'], 'core': '18432.a1', 'coset_action_label': '36T11647', 'count': 36, 'diagramx': [7399, -1, 8679, -1], 'generators': [87181926493, 1313941680016, 1313941673647, 11300046513967, 87102720, 127387560, 23, 4103734078080, 5606321841949], 'label': '18432.q.36.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '36.h1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.H', 'subgroup_fusion': None, 'weyl_group': '512.39163'}
  • id: 63387865
    {'ambient': '18432.q', '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': ['48.W', '96.H'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [487, -1, 343, -1], 'generators': [1314028776367, 6611, 11543, 2789792409600, 6920263519898, 16687], 'label': '18432.q.192.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.H', 'old_label': '192.g1', 'projective_image': '18432.q', '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': '48.48'}
  • id: 63387866
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BB', '96.U'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3256, -1, 1212, -1], 'generators': [16696, 127382407, 5183, 1313941668480, 4103646992063, 843], 'label': '18432.q.192.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.U', 'old_label': '192.h1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.H', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63387867
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.S', '96.A', '96.C', '96.E'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3555, -1, 2062, -1], 'generators': [40284840, 6227384421, 6611, 11520, 1313941668480, 5160], 'label': '18432.q.192.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '192.i1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.I', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387868
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.U', '96.A', '96.D', '96.F'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3625, -1, 2118, -1], 'generators': [40284840, 6611, 11520, 1313941668480, 5160, 6354044781], 'label': '18432.q.192.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '192.j1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.J', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387869
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.U', '96.B', '96.C', '96.F'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3578, -1, 2141, -1], 'generators': [40284840, 6611, 4097380065261, 11520, 1313941668480, 5160], 'label': '18432.q.192.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '192.k1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.K', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387870
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.T', '96.B', '96.D', '96.E'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3532, -1, 2019, -1], 'generators': [40284840, 6611, 4097506695141, 11520, 1313941668480, 5160], 'label': '18432.q.192.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '192.l1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.L', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387871
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.D', '96.BC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1622, -1, 59, -1], 'generators': [174363845160, 4103734078080, 16, 1313941668480, 5160, 8396027160338], 'label': '18432.q.192.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BC', 'old_label': '192.m1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.M', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 63387872
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.E', '96.Y'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3513, -1, 1862, -1], 'generators': [6227384421, 5167, 1314028771216, 860, 11536, 40284847], 'label': '18432.q.192.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.Y', 'old_label': '192.n1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.N', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387873
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BC', '96.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1459, -1, 1162, -1], 'generators': [4103734078080, 5606321847709, 6314490842, 6603, 40279680, 1313941668480], 'label': '18432.q.192.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.J', 'old_label': '192.o1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.O', 'subgroup_fusion': None, 'weyl_group': '96.144'}
  • id: 63387874
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BD', '96.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [2348, -1, 1097, -1], 'generators': [4103734078080, 40279680, 1313941668480, 8396027160338, 6314475602, 843], 'label': '18432.q.192.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.J', 'old_label': '192.p1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.P', 'subgroup_fusion': None, 'weyl_group': '96.144'}
  • id: 63387875
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.A'], 'contains': ['72.BB', '72.BD', '72.BF', '72.BH', '72.BU', '72.BW', '72.BY'], 'core': '18432.a1', 'coset_action_label': '36T11668', 'count': 18, 'diagramx': [9262, -1, 9405, -1], 'generators': [23, 1313941680016, 1313941673647, 87181920741, 87107887, 12694932195247, 127387560, 4103734078080, 5606321841949], 'label': '18432.q.36.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.i1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.I', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387876
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BE', '96.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [919, -1, 1005, -1], 'generators': [4103734078080, 6227384402, 40279680, 1313941668480, 8396027160338, 843], 'label': '18432.q.192.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.J', 'old_label': '192.q1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.Q', 'subgroup_fusion': None, 'weyl_group': '96.144'}
  • id: 63387877
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BF', '96.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1832, -1, 1125, -1], 'generators': [4103734078080, 5606321847709, 6603, 6227399642, 40279680, 1313941668480], 'label': '18432.q.192.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.J', 'old_label': '192.r1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.R', 'subgroup_fusion': None, 'weyl_group': '96.144'}
  • id: 63387878
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BO', '96.E', '96.F', '96.N'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3495, -1, 1997, -1], 'generators': [4103734078080, 16, 1313941668480, 87091216, 843, 7], 'label': '18432.q.192.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '192.s1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.S', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63387879
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.F', '64.A', '96.BC'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [2667, -1, 36, -1], 'generators': [174363851543, 4103734078080, 11543, 1313941668480, 8396027160338, 16687], 'label': '18432.q.192.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BC', 'old_label': '192.t1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.T', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 63387880
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BJ', '64.A', '96.H'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [867, -1, 170, -1], 'generators': [4103734078080, 11543, 1313941668480, 8396027160338, 843, 16687], 'label': '18432.q.192.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '192.u1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.U', 'subgroup_fusion': None, 'weyl_group': '288.1024'}
  • id: 63387881
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BN', '96.H', '96.I'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [844, -1, 565, -1], 'generators': [4103734078080, 6611, 11543, 5606321851418, 1313941668480, 16687], 'label': '18432.q.192.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.G', 'old_label': '192.v1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.V', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387882
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BO', '96.H', '96.I', '96.U'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [940, -1, 1191, -1], 'generators': [4103734078080, 16696, 87096383, 5183, 1313941668480, 843], 'label': '18432.q.192.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.G', 'old_label': '192.w1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.W', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63387883
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BH', '64.B', '96.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3211, -1, 90, -1], 'generators': [5606234750738, 16, 5167, 11536, 174363856696, 7], 'label': '18432.q.192.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.J', 'old_label': '192.x1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.X', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 63387884
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['64.C', '96.K', '96.Q', '96.BE'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [894, -1, 248, -1], 'generators': [4103734078080, 174363840000, 40279680, 1313941668480, 5606321841938, 87091200], 'label': '18432.q.192.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.D', 'old_label': '192.y1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.Y', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387885
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.G', '48.BI', '64.C', '96.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3237, -1, 269, -1], 'generators': [4103734078080, 40279680, 1313941668480, 5606321841938, 87091200, 843], 'label': '18432.q.192.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.A', 'old_label': '192.z1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.Z', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 63387886
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.A'], 'contains': ['72.BC', '72.BE', '72.BG', '72.BI', '72.BU', '72.BW', '72.BZ'], 'core': '18432.a1', 'coset_action_label': '36T11662', 'count': 18, 'diagramx': [9240, -1, 9349, -1], 'generators': [23, 4103734078080, 127387560, 5606321847717, 87107887, 87181920741, 11300123081647, 1313941673647, 1313941680016], 'label': '18432.q.36.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.j1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.J', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387887
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['64.B', '96.K', '96.BF'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [540, -1, 226, -1], 'generators': [16, 5167, 11536, 8396027160338, 843, 7], 'label': '18432.q.192.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '192.ba1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BA', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387888
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.A', '48.BK', '64.D', '96.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3681, -1, 1675, -1], 'generators': [4103734078080, 6227384421, 40279680, 1313941668480, 860, 87091200], 'label': '18432.q.192.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.J', 'old_label': '192.bb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BB', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 63387889
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['64.D', '96.K', '96.L', '96.BG'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2792, -1, 1555, -1], 'generators': [6227384421, 16, 5167, 11536, 843, 7], 'label': '18432.q.192.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.A', 'old_label': '192.bc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BC', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387890
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.C', '48.BM', '64.D'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [4128, -1, 2173, -1], 'generators': [6227384421, 16, 93409309459, 5167, 11536, 7], 'label': '18432.q.192.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.BD', 'old_label': '192.bd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BD', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387891
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['96.L', '96.M', '96.O', '96.S', '96.T', '96.BK', '96.BL'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2920, -1, 1716, -1], 'generators': [16, 87102720, 5167, 11536, 843, 7], 'label': '18432.q.192.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '192.be1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BE', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387892
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['96.Q', '96.R', '96.S', '96.T', '96.V', '96.BL', '96.BM'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [995, -1, 720, -1], 'generators': [16, 5167, 1314028771200, 11536, 843, 7], 'label': '18432.q.192.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '192.bf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BF', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63387893
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BL', '64.E', '96.E'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3425, -1, 1980, -1], 'generators': [4103734078080, 6227384421, 16, 1313941668480, 843, 7], 'label': '18432.q.192.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.E', 'old_label': '192.bg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BG', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387894
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.B', '64.E', '96.Y'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3733, -1, 1933, -1], 'generators': [6227384421, 87102736, 5167, 860, 11536, 40284847], 'label': '18432.q.192.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.Y', 'old_label': '192.bh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BH', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387895
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.C', '48.H', '48.BM', '64.E'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [4248, -1, 2812, -1], 'generators': [4103734078080, 6227384421, 16, 93409309459, 1313941668480, 7], 'label': '18432.q.192.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.BI', 'old_label': '192.bi1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BI', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387896
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.C', '48.H', '48.BR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [4850, -1, 4164, -1], 'generators': [6227384421, 93409309459, 2789705329920, 5167, 11536, 4103606723896], 'label': '18432.q.192.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.BJ', 'old_label': '192.bj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BJ', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387897
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.A'], 'contains': ['72.T', '72.V', '72.BB', '72.BC', '72.BF', '72.BG', '72.CV', '72.DA', '72.DD', '72.DX', '72.DZ'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [9217, -1, 9370, -1], 'generators': [8396027160338, 23, 11300123081647, 11536, 1313941668480, 5167, 127387560, 87181926490, 4103734078080], 'label': '18432.q.36.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.k1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.K', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387898
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.H', '48.BM'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [4264, -1, 4058, -1], 'generators': [6227384421, 93409309459, 5167, 2789792409616, 11536, 4103734078087], 'label': '18432.q.192.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.BK', 'old_label': '192.bk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BK', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387899
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BA', '96.Y', '96.Z', '96.BV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3443, -1, 1793, -1], 'generators': [87102736, 5167, 1313941668480, 11536, 40284847, 843], 'label': '18432.q.192.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BK', 'old_label': '192.bl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BL', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 63387900
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.W', '96.BA', '96.BB', '96.BQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [150, -1, 1262, -1], 'generators': [6920176419218, 5167, 2789792409600, 11536, 4103646998416, 843], 'label': '18432.q.192.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.bm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BM', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387901
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.V', '96.BB', '96.BC', '96.BP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [352, -1, 809, -1], 'generators': [16703, 4103734078080, 174440412856, 1313941668480, 5176, 8396027160338], 'label': '18432.q.192.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '192.bn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BN', 'subgroup_fusion': None, 'weyl_group': '96.195'}
  • id: 63387902
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.X', '96.BA', '96.BB', '96.BR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [212, -1, 1297, -1], 'generators': [4103693803567, 5167, 4097506695141, 1313941668480, 11536, 851], 'label': '18432.q.192.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.bo1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BO', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387903
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.Y', '96.BA', '96.BD', '96.BP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [326, -1, 889, -1], 'generators': [16703, 4103734078080, 174440412856, 1313941668480, 8396027166106, 5176], 'label': '18432.q.192.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '192.bp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BP', 'subgroup_fusion': None, 'weyl_group': '96.195'}
  • id: 63387904
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.Z', '96.BC', '96.BD', '96.BS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [966, -1, 291, -1], 'generators': [8396027169818, 16703, 5176, 1313941668480, 4103734078080, 174440412856], 'label': '18432.q.192.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BH', 'old_label': '192.bq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BQ', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 63387905
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BB', '96.BC', '96.BD', '96.BV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2229, -1, 316, -1], 'generators': [4103693803567, 5167, 1313941668480, 11536, 4103646998416, 843], 'label': '18432.q.192.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BH', 'old_label': '192.br1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BR', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63387906
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['96.BE', '96.BF', '96.BG', '96.BH', '96.BI', '96.BJ', '96.BK', '96.BL', '96.BM', '96.BW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [442, -1, 1068, -1], 'generators': [16, 5167, 1313941668480, 11536, 843, 7], 'label': '18432.q.192.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '192.bs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BS', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387907
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.Q', '96.BN', '96.BO', '96.BP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [259, -1, 1395, -1], 'generators': [23, 16703, 4103734078080, 1313941668480, 8396027166106, 174440407703], 'label': '18432.q.192.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.bt1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BT', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387908
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.A'], 'contains': ['72.BD', '72.BE', '72.BH', '72.BI', '72.CV', '72.DC', '72.DD'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [9419, -1, 9470, -1], 'generators': [23, 4103734078080, 87181926490, 127387560, 5606321841949, 5167, 1313941668480, 11536, 11300123081647], 'label': '18432.q.36.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.l1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.L', 'subgroup_fusion': None, 'weyl_group': '512.152421'}
  • id: 63387909
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.R', '96.BN', '96.BO', '96.BQ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [171, -1, 1419, -1], 'generators': [87102736, 5167, 2789792409600, 11536, 8396027160338, 843], 'label': '18432.q.192.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.bu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BU', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387910
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.S', '96.Y', '96.BN', '96.BR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [505, -1, 1693, -1], 'generators': [6227384421, 5167, 1313941668480, 11536, 851, 40284847], 'label': '18432.q.192.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '192.bv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BV', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 63387911
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.T', '96.Z', '96.BO', '96.BR'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [468, -1, 1587, -1], 'generators': [5167, 4097506695141, 1313941668480, 11536, 851, 40284847], 'label': '18432.q.192.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '192.bw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BW', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 63387912
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.U', '96.Y', '96.Z', '96.BU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3466, -1, 1835, -1], 'generators': [5167, 1313941668480, 11536, 6314485093, 40284847, 843], 'label': '18432.q.192.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BK', 'old_label': '192.bx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BX', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387913
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.I', '96.BB', '96.BN', '96.CA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [68, -1, 1436, -1], 'generators': [5606275036186, 6266944090, 5167, 1313941668480, 11536, 843], 'label': '18432.q.192.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.by1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BY', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387914
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.J', '96.BB', '96.BO', '96.CA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [26, -1, 1334, -1], 'generators': [9709928554906, 5167, 1313941668480, 11536, 4097467146970, 843], 'label': '18432.q.192.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.bz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.BZ', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387915
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.K', '96.BA', '96.BN', '96.CB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [192, -1, 1351, -1], 'generators': [6920176419218, 6266944090, 5167, 1313941668480, 11536, 843], 'label': '18432.q.192.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.ca1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CA', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387916
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.L', '96.BA', '96.BO', '96.CB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [88, -1, 1313, -1], 'generators': [5167, 1313941668480, 11536, 8396027160338, 4097467146970, 843], 'label': '18432.q.192.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.cb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CB', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387917
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.M', '96.BB', '96.BN', '96.CB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [236, -1, 1280, -1], 'generators': [6266944090, 5167, 1313941668480, 11536, 8396027160338, 843], 'label': '18432.q.192.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.cc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CC', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387918
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.N', '96.BB', '96.BO', '96.CB'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [119, -1, 1249, -1], 'generators': [6920176419218, 5167, 1313941668480, 11536, 4097467146970, 843], 'label': '18432.q.192.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.cd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CD', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387919
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.B'], 'contains': ['72.U', '72.W', '72.CW', '72.DF', '72.DI'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8756, -1, 7869, -1], 'generators': [8396027166098, 11300079536047, 11536, 1313941668480, 5167, 87258503650, 127387560, 23, 4103734078080], 'label': '18432.q.36.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.m1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.M', 'subgroup_fusion': None, 'weyl_group': '512.39163'}
  • id: 63387920
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.O', '96.BA', '96.BN', '96.CA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [50, -1, 1459, -1], 'generators': [9709928554906, 6266944090, 5167, 1313941668480, 11536, 843], 'label': '18432.q.192.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.ce1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CE', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387921
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.P', '96.BA', '96.BO', '96.CA'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5, -1, 1371, -1], 'generators': [5606275036186, 5167, 1313941668480, 11536, 4097467146970, 843], 'label': '18432.q.192.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.cf1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CF', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387922
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BO', '96.BP', '96.BQ', '96.BR', '96.BS', '96.BT', '96.BU', '96.BV'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [559, -1, 1516, -1], 'generators': [4103734078080, 87102736, 5167, 1313941668480, 11536, 843], 'label': '18432.q.192.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '192.cg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CG', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387923
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BP', '64.F', '96.BZ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 96, 'diagramx': [5035, -1, 4699, -1], 'generators': [4103734078080, 93409309459, 19615115146917, 5167, 1313941668480, 11536], 'label': '18432.q.192.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BZ', 'old_label': '192.ch1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CH', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387924
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BQ', '64.F', '96.BZ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 32, 'diagramx': [5058, -1, 4720, -1], 'generators': [4103734078080, 5167, 1313941668480, 20835607967277, 93528701300, 11536], 'label': '18432.q.192.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.E', 'old_label': '192.ci1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CI', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
  • id: 63387925
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BG', '64.G', '96.BP', '96.CA', '96.CB'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 48, 'diagramx': [302, -1, 1233, -1], 'generators': [4103734078080, 174400139536, 5167, 1313941668480, 11536, 8396027160338], 'label': '18432.q.192.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.cj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CJ', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387926
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BJ', '64.G', '96.BQ', '96.CB'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 8, 'diagramx': [418, -1, 934, -1], 'generators': [4103734078080, 5167, 1313941668480, 11536, 8396027160338, 843], 'label': '18432.q.192.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.B', 'old_label': '192.ck1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CK', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 63387927
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BL', '64.H', '96.BR', '96.CA', '96.CB'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 48, 'diagramx': [399, -1, 1569, -1], 'generators': [4103734078080, 6227384421, 5167, 1313941668480, 11536, 851], 'label': '18432.q.192.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.BE', 'old_label': '192.cl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CL', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 63387928
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BM', '48.BR', '64.H', '96.BZ'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 96, 'diagramx': [4313, -1, 4539, -1], 'generators': [4103734078080, 6227384421, 93409309459, 5167, 1313941668480, 11536], 'label': '18432.q.192.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.BZ', 'old_label': '192.cm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CM', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387929
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BN', '96.BQ', '96.BT', '96.CA'], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 24, 'diagramx': [380, -1, 1485, -1], 'generators': [4103734078080, 9709928554906, 5167, 1313941668480, 11536, 843], 'label': '18432.q.192.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '192.cn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CN', 'subgroup_fusion': None, 'weyl_group': '192.1472'}
  • id: 63387930
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.B'], 'contains': ['72.CW', '72.DH', '72.DI', '72.DY', '72.EA'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8785, -1, 8038, -1], 'generators': [11300079536047, 11536, 1313941668480, 5167, 87258503650, 127387560, 23, 4103734078080, 5606321847709], 'label': '18432.q.36.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.n1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.N', 'subgroup_fusion': None, 'weyl_group': '512.39163'}
  • id: 63387931
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BM', '48.BU', '48.BX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [4914, -1, 4396, -1], 'generators': [6227384421, 2789792421136, 93409309459, 4103734083247, 11520, 5160], 'label': '18432.q.192.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.CO', 'old_label': '192.co1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CO', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387932
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BP', '96.CH'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5006, -1, 5577, -1], 'generators': [2789792421136, 4103734083247, 19615115146917, 93409305135, 87091216, 127370887], 'label': '18432.q.192.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CH', 'old_label': '192.cp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CP', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387933
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BQ', '48.BT', '96.CH'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5104, -1, 5015, -1], 'generators': [4103734083247, 19440678730917, 93409310291, 87091223, 127370887, 1313941680016], 'label': '18432.q.192.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CH', 'old_label': '192.cq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CQ', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387934
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BR', '48.BU', '96.CH'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4930, -1, 4597, -1], 'generators': [6227384421, 2789792421136, 93409309459, 4103734083247, 87091216, 127370887], 'label': '18432.q.192.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CH', 'old_label': '192.cr1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CR', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387935
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BQ', '48.BT', '48.BW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [5238, -1, 4750, -1], 'generators': [4103734089616, 19440678730917, 93409319540, 127376040, 87107880, 2789792414767], 'label': '18432.q.192.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.CS', 'old_label': '192.cs1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CS', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387936
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BQ', '48.BW', '96.CI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5120, -1, 4808, -1], 'generators': [4103734083247, 20835487844517, 93409319540, 127376040, 87107880, 1313941680016], 'label': '18432.q.192.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CI', 'old_label': '192.ct1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CT', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387937
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BP', '48.BS', '48.BV', '96.CI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5141, -1, 4672, -1], 'generators': [2789792421136, 87102720, 4103734083247, 19615115146917, 93409305135, 127376040], 'label': '18432.q.192.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CI', 'old_label': '192.cu1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CU', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387938
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.BR', '48.BX', '96.CI'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4946, -1, 4612, -1], 'generators': [6227384421, 2789792421136, 87102720, 93409309459, 4103734083247, 127376040], 'label': '18432.q.192.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CI', 'old_label': '192.cv1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CV', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387939
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BP'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [5081, -1, 4904, -1], 'generators': [2789792421136, 127387576, 87096383, 4103734083247, 19615115146917, 93409305135], 'label': '18432.q.192.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.CW', 'old_label': '192.cw1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CW', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63387940
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.E', '96.C'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3644, -1, 2159, -1], 'generators': [6227384421, 1314028759696, 16, 1313988480023, 843, 7], 'label': '18432.q.192.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.C', 'old_label': '192.cx1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CX', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387941
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.A'], 'contains': ['12.E', '12.F', '12.J', '18.E', '24.T', '24.U'], 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5194, -1, 4646, -1], 'generators': [11536, 16, 93409309459, 127387560, 4103734078080, 5167, 19615115146917, 7, 1313941668480, 87102720, 6227384421], 'label': '18432.q.6.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '6.a1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 63387942
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.E'], 'contains': ['72.BK', '72.BR', '72.DJ', '72.DN', '72.DO'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6412, -1, 6769, -1], 'generators': [4103734078080, 127387560, 20835531390117, 87102736, 180591240241, 5167, 1313941668480, 11536, 7], 'label': '18432.q.36.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '36.o1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.O', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387943
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.E', '96.A'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3719, -1, 2100, -1], 'generators': [6227384421, 6611, 11520, 5160, 1314028771200, 1313988496680], 'label': '18432.q.192.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.A', 'old_label': '192.cy1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CY', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387944
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.CZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BS', '64.I'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [7468, -1, 4127, -1], 'generators': [4103647003567, 1313988485176, 2615428580524, 19615115146917, 11543, 16687], 'label': '18432.q.192.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.CZ', 'old_label': '192.cz1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.CZ', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63387945
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BT', '64.I'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [7491, -1, 4432, -1], 'generators': [16696, 93409310300, 1314028764863, 20835531399586, 5183, 2789745609607], 'label': '18432.q.192.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.I', 'old_label': '192.da1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DA', 'subgroup_fusion': None, 'weyl_group': '288.1025'}
  • id: 63387946
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.C', '48.H', '48.BU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [4882, -1, 4194, -1], 'generators': [6227384421, 93409309459, 127382407, 11520, 5160, 87091216], 'label': '18432.q.192.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.DB', 'old_label': '192.db1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DB', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387947
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.C', '48.H', '48.BX'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [4866, -1, 4179, -1], 'generators': [6227384421, 16, 87102720, 93409309459, 127376056, 7], 'label': '18432.q.192.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.DC', 'old_label': '192.dc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DC', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387948
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.B', '64.J', '96.C'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3748, -1, 2201, -1], 'generators': [127370903, 6227384421, 16, 87091216, 843, 7], 'label': '18432.q.192.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.C', 'old_label': '192.dd1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DD', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387949
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.C', '48.BU', '64.J'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [4280, -1, 4106, -1], 'generators': [127370903, 6227384421, 16, 93409309459, 87091216, 7], 'label': '18432.q.192.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.DE', 'old_label': '192.de1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DE', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387950
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BV', '64.K', '96.CJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [5717, -1, 4475, -1], 'generators': [2789705318416, 16, 2615428580524, 19615115146917, 4103606707223, 7], 'label': '18432.q.192.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CJ', 'old_label': '192.df1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DF', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387951
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BW', '64.K', '96.CJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [5740, -1, 4496, -1], 'generators': [2789705318416, 2615428576220, 20835531393818, 16, 4103606707223, 7], 'label': '18432.q.192.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.I', 'old_label': '192.dg1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DG', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
  • id: 63387952
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.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': ['48.B', '64.L', '96.A'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3764, -1, 2187, -1], 'generators': [6227384421, 6611, 127387560, 87102720, 11520, 5160], 'label': '18432.q.192.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.A', 'old_label': '192.dh1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DH', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63387953
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.A', '18.B', '18.E'], 'contains': ['72.X', '72.Y', '72.BJ', '72.BL', '72.BP', '72.BU', '72.BV', '72.CV', '72.CW', '72.DJ', '72.DL', '72.EB', '72.EC'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [8527, -1, 7908, -1], 'generators': [18301133924517, 4103734078080, 127387560, 87102736, 5167, 180591240257, 1313941668480, 11536, 7], 'label': '18432.q.36.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.p1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.P', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387954
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.C', '48.BX', '64.L', '96.CJ'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [4978, -1, 4149, -1], 'generators': [2789705318416, 6227384421, 16, 93409309459, 4103606707223, 7], 'label': '18432.q.192.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CJ', 'old_label': '192.di1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DI', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387955
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.H', '48.BU'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [4898, -1, 4295, -1], 'generators': [2789792421120, 6227384421, 93409309459, 4103734083240, 2789745609607, 87091216], 'label': '18432.q.192.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.DJ', 'old_label': '192.dj1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DJ', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387956
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [5282, -1, 4561, -1], 'generators': [127370903, 4103734089623, 2615428580524, 2789792426287, 19615115146917, 1314028764863], 'label': '18432.q.192.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.DK', 'old_label': '192.dk1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DK', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63387957
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BV'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [5199, -1, 4645, -1], 'generators': [87102720, 4103606718727, 2615428580524, 19615115146917, 1313941680023, 4103734094767], 'label': '18432.q.192.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.DL', 'old_label': '192.dl1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DL', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63387958
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BV', '96.CK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [5169, -1, 4787, -1], 'generators': [87102720, 2615428580524, 19615115146917, 2789792409616, 4103734078087, 2789745603256], 'label': '18432.q.192.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CK', 'old_label': '192.dm1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DM', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387959
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BT', '48.BW', '96.CK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [5222, -1, 4765, -1], 'generators': [2789792414760, 4103647003567, 1313988485176, 4103734089600, 1488305515100, 20835531384349], 'label': '18432.q.192.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CK', 'old_label': '192.dn1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DN', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387960
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.H', '48.BX', '96.CK'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [4962, -1, 4582, -1], 'generators': [2789792421120, 2789705318416, 6227384421, 1313988491527, 93409309459, 4103734083240], 'label': '18432.q.192.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.CK', 'old_label': '192.do1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DO', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 63387961
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.BT', '48.BW'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [5260, -1, 4735, -1], 'generators': [127387560, 87102720, 20835531390117, 4010324781020, 1313941673663, 4103734094776], 'label': '18432.q.192.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.DP', 'old_label': '192.dp1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DP', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 63387962
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '192.DQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.BS'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 384, 'diagramx': [5634, -1, 4518, -1], 'generators': [1313941673640, 4103647003567, 2789745598103, 2615428580524, 19615115146917, 4103734089600], 'label': '18432.q.192.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.DQ', 'old_label': '192.dq1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.DQ', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63387963
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.B', '64.G', '128.D'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [3481, -1, 439, -1], 'generators': [5167, 11536, 93485161460, 9709968828818, 843], 'label': '18432.q.256.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.D', 'old_label': '256.a1', 'projective_image': '18432.q', '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': '48.48'}
  • id: 63387964
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.F'], 'contains': ['72.CX', '72.CZ', '72.DE', '72.DG', '72.DK', '72.DM', '72.DO'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2893, -1, 4055, -1], 'generators': [4103734078080, 6227384410, 127387576, 87102720, 5606321841949, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.36.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '36.q1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.Q', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387965
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.A', '64.C', '64.G', '128.D'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [3412, -1, 274, -1], 'generators': [4103734078080, 93485146443, 1313941668480, 8396027160338, 843], 'label': '18432.q.256.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.D', 'old_label': '256.b1', 'projective_image': '18432.q', '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': '144.183'}
  • id: 63387966
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.D', '64.E', '64.H', '128.D'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [3898, -1, 1769, -1], 'generators': [6227384421, 5167, 93528701300, 11536, 851], 'label': '18432.q.256.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '128.D', 'old_label': '256.c1', 'projective_image': '18432.q', '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': '144.183'}
  • id: 63387967
    {'ambient': '18432.q', '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': 1, 'contained_in': ['64.A', '64.B'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [3380, -1, 28, -1], 'generators': [5606234750738, 11543, 93409319531, 843, 16687], 'label': '18432.q.256.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '256.D', 'old_label': '256.d1', 'projective_image': '18432.q', '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': '24.12'}
  • id: 63387968
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.D', '64.E', '64.J', '64.L'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [4177, -1, 2896, -1], 'generators': [6227384421, 93409304532, 16, 843, 7], 'label': '18432.q.256.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '256.E', 'old_label': '256.e1', 'projective_image': '18432.q', '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': '72.43'}
  • id: 63387969
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.F'], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [5249, -1, 7321, -1], 'generators': [5606234750738, 10092, 1307714285522, 11219048432047, 1488305518572], 'label': '18432.q.256.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '256.F', 'old_label': '256.f1', 'projective_image': '18432.q', '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': '72.40'}
  • id: 63387970
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '1152.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': [], 'core': '1152.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5186, -1, 5382], 'generators': [4103734078080, 5167, 1313941668480, 11536], 'label': '18432.q.1152.A', 'mobius_quo': -1, 'mobius_sub': None, 'normal_closure': '1152.A', 'normal_contained_in': ['72.A'], 'normal_contains': ['18432.a1'], 'normalizer': '1.a1', 'old_label': '1152.a1.N', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.A', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 63387971
    {'ambient': '18432.q', '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': '2048.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 256, 'diagramx': None, 'generators': [93485146443, 843], 'label': '18432.q.2048.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '256.F', 'old_label': '2048.a1', 'projective_image': '18432.q', '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': '8.3'}
  • id: 63387972
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '18432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': [], 'core': '18432.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5186, -1, 5382], 'generators': [], 'label': '18432.q.18432.a1', 'mobius_quo': 1, 'mobius_sub': None, 'normal_closure': '18432.a1', 'normal_contained_in': ['1152.A'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '18432.a1.N', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18432.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63387973
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.A', '18.C', '18.F'], 'contains': ['72.BM', '72.BN', '72.BW', '72.BX', '72.CD', '72.CE', '72.CY', '72.DA', '72.DC', '72.DK', '72.DL'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7546, -1, 8609, -1], 'generators': [4103734078080, 6227384421, 127387576, 87102720, 5606321841949, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.36.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.r1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.R', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387974
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.B', '18.D', '18.F'], 'contains': ['72.DB', '72.DF', '72.DH', '72.DL', '72.DM'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7516, -1, 6914, -1], 'generators': [4103734078080, 6227384421, 127387576, 87102720, 5606321851429, 5167, 1313941668480, 11536, 127387567], 'label': '18432.q.36.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.s1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.S', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387975
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.C', '18.D', '18.E'], 'contains': ['72.BO', '72.BS', '72.DL', '72.DN'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7242, -1, 7415, -1], 'generators': [4103734078080, 127387560, 20835531390117, 87102736, 5167, 180591240257, 1313941668480, 11536, 7], 'label': '18432.q.36.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.t1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.T', 'subgroup_fusion': None, 'weyl_group': '512.51562'}
  • id: 63387976
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.A', '18.D', '18.G'], 'contains': ['72.BQ', '72.BY', '72.BZ', '72.DD', '72.DL'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7661, -1, 7950, -1], 'generators': [4103734078080, 127387560, 11219048432047, 87102720, 6227383801, 5167, 1313941668480, 11536, 7], 'label': '18432.q.36.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.u1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.U', 'subgroup_fusion': None, 'weyl_group': '512.51574'}
  • id: 63387977
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['18.B', '18.C', '18.G'], 'contains': ['72.BT', '72.CA', '72.DI', '72.DL'], 'core': '1152.A', 'coset_action_label': None, 'count': 9, 'diagramx': [7593, -1, 7928, -1], 'generators': [4103734078080, 127387560, 87102720, 6227383801, 5167, 1313941668480, 11536, 11219135523247, 7], 'label': '18432.q.36.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.v1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.V', 'subgroup_fusion': None, 'weyl_group': '512.51574'}
  • id: 63387978
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['12.B', '18.F'], 'contains': ['72.CX', '72.CY', '72.DE', '72.DF', '72.DR', '72.DU', '72.DW'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3072, -1, 4037, -1], 'generators': [40284840, 4103734078080, 16, 5167, 1313941668480, 9709928549146, 11536, 6354044781, 7], 'label': '18432.q.36.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '36.w1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.W', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387979
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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': ['12.A', '18.F'], 'contains': ['72.CY', '72.CZ', '72.DG', '72.DH', '72.DS', '72.DV', '72.DW'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2918, -1, 4073, -1], 'generators': [40284840, 4103734078080, 16, 5606321841949, 5167, 1313941668480, 11536, 6354044781, 7], 'label': '18432.q.36.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '36.x1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.X', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387980
    {'ambient': '18432.q', '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': ['2.B'], 'contains': ['12.A', '12.B', '12.C', '12.D', '12.G', '12.H', '12.I', '18.F', '24.J'], 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2145, -1, 1542, -1], 'generators': [11536, 16, 5606321841949, 843, 127387560, 4103734078080, 5167, 7, 1313941668480, 87102720, 6227384421], 'label': '18432.q.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '6.b1', 'projective_image': '18432.q', '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': '1536.408560345'}
  • id: 63387981
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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.C', '18.F'], 'contains': ['72.CB', '72.CC', '72.CF', '72.CG', '72.CL', '72.CM', '72.CN', '72.CO', '72.CT', '72.CU', '72.CX', '72.CZ', '72.DA', '72.DB', '72.DP', '72.DQ', '72.DR', '72.DS', '72.DT'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2159, -1, 3208, -1], 'generators': [40284840, 4103734078080, 6227384421, 16, 5167, 1313941668480, 9709928549146, 11536, 7], 'label': '18432.q.36.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '36.y1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.Y', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387982
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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.D', '18.F'], 'contains': ['72.DB', '72.DC', '72.DE', '72.DG', '72.DT', '72.DU', '72.DV'], 'core': '1152.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2842, -1, 3867, -1], 'generators': [40284840, 4103734078080, 6227384421, 16, 5606321841949, 5167, 1313941668480, 11536, 7], 'label': '18432.q.36.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '36.z1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.Z', 'subgroup_fusion': None, 'weyl_group': '256.8935'}
  • id: 63387983
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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.E', '12.F', '18.E'], 'contains': ['72.A', '72.N', '72.P', '72.Z', '72.BA', '72.DJ', '72.DN'], 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6128, -1, 5862, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 20835531390117, 5167, 1313941668480, 11536, 7], 'label': '18432.q.36.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '36.ba1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BA', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 63387984
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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.G', '12.H', '18.F'], 'contains': ['72.A', '72.CJ', '72.CK', '72.CR', '72.CS', '72.DK', '72.DM', '72.DR', '72.DS', '72.DU', '72.DV'], 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2774, -1, 2059, -1], 'generators': [4103734078080, 127387560, 16, 87102720, 5606321841949, 5167, 1313941668480, 11536, 7], 'label': '18432.q.36.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '36.bb1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BB', 'subgroup_fusion': None, 'weyl_group': '192.1488'}
  • id: 63387985
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '36.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.I', '12.J', '18.E', '18.F', '18.G'], 'contains': ['72.A', '72.O', '72.Q', '72.R', '72.S', '72.CH', '72.CI', '72.CP', '72.CQ', '72.DL', '72.DO', '72.DT', '72.DW'], 'core': '72.A', 'coset_action_label': None, 'count': 9, 'diagramx': [4702, -1, 5155, -1], 'generators': [4103734078080, 6227384421, 127387560, 16, 87102720, 5167, 1313941668480, 11536, 7], 'label': '18432.q.36.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bc1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BC', 'subgroup_fusion': None, 'weyl_group': '128.753'}
  • id: 63387986
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.I', '16.A'], 'contains': ['96.A', '96.B', '96.C', '96.D', '96.E', '96.F', '96.N', '144.GM', '192.BB'], 'core': '18432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3684, -1, 2076, -1], 'generators': [6227384421, 5160, 11520, 87102720, 127387560, 6611, 1313941668480, 4103734078080], 'label': '18432.q.48.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.A', 'old_label': '48.a1', 'projective_image': '18432.q', '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': '96.226'}
  • id: 63387987
    {'ambient': '18432.q', 'aut_centralizer_order': None, 'aut_label': '48.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.A', '24.E'], 'contains': ['96.L', '96.M', '96.O', '144.GM', '192.BH', '192.DD', '192.DH'], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3787, -1, 1958, -1], 'generators': [6227384421, 7, 843, 87102720, 16, 127387560, 5167, 11536], 'label': '18432.q.48.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.E', 'old_label': '48.b1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.B', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
  • id: 63387988
    {'ambient': '18432.q', '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': '18432.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.J', '16.A'], 'contains': ['96.P', '144.GM', '192.BD', '192.BI', '192.BJ', '192.DB', '192.DC', '192.DE', '192.DI'], 'core': '18432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4275, -1, 4108, -1], 'generators': [6227384421, 127387560, 16, 87102720, 93409309459, 5167, 11536, 7], 'label': '18432.q.48.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.C', 'old_label': '48.c1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.C', 'subgroup_fusion': None, 'weyl_group': '384.20164'}
  • id: 63387989
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.G'], 'contains': ['96.Q', '96.R', '96.S', '144.GN', '192.M'], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1497, -1, 220, -1], 'generators': [4103734078080, 87102720, 174363840007, 5606321841949, 127382407, 11520, 1313941668480, 7], 'label': '18432.q.48.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.G', 'old_label': '48.d1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.D', 'subgroup_fusion': None, 'weyl_group': '192.1000'}
  • id: 63387990
    {'ambient': '18432.q', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.E'], 'contains': ['96.L', '96.M', '96.T', '144.GO', '192.N', '192.CX', '192.CY'], 'core': '18432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3615, -1, 1893, -1], 'generators': [6227384421, 16, 5167, 1314028771200, 11536, 1313988496680, 843, 7], 'label': '18432.q.48.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.E', 'old_label': '48.e1', 'projective_image': '18432.q', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.E', 'subgroup_fusion': None, 'weyl_group': '192.1538'}