Abstract group data - 256.29702

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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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [4, 4, 8, 4, 2, 4], 'aut_gens': [[1, 2, 4, 8, 16, 64], [13, 10, 36, 136, 80, 96], [137, 130, 14, 8, 212, 226], [39, 34, 174, 136, 54, 98], [37, 2, 36, 136, 216, 72], [41, 138, 4, 8, 184, 104], [13, 2, 164, 136, 112, 104]], 'aut_group': None, 'aut_hash': 3543113139147162601, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 262144, 'aut_permdeg': 48, 'aut_perms': [10125608149357834087786787837263927135294011410880419837515636, 4476121807736157849370587672641079242474340191902329310572798, 10325747835271930861775008239730240390388010669397547015558001, 5470822308334020599919499122281503567907676262790285642807313, 2078219406896991183758015250565587669518325693914118141163730, 10339907862070628219009650321469034129857550222196872351698643], 'aut_phi_ratio': 2048.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 1, 4, 1], [2, 2, 4, 1], [2, 4, 2, 2], [2, 4, 4, 1], [2, 4, 8, 1], [2, 8, 2, 1], [4, 4, 4, 1], [4, 8, 2, 1], [4, 8, 4, 2], [4, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^{12}.C_2^5.C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': None, 'autcent_hash': 3946057693156513511, 'autcent_nilpotent': True, 'autcent_order': 32768, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{15}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '8.3', 'autcentquo_hash': 3, 'autcentquo_nilpotent': True, 'autcentquo_order': 8, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [2, 4, 16], [2, 8, 2], [4, 4, 4], [4, 8, 18]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, 'central_quotient': '32.51', 'commutator_count': 1, 'commutator_label': '8.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 29702, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [2, 4, 1, 16], [2, 8, 1, 2], [4, 4, 1, 4], [4, 8, 1, 18]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1249920, 'exponent': 4, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '32.51', 'hash': 29702, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 1, 2, 2], 'inner_gens': [[1, 2, 4, 8, 176, 72], [1, 2, 4, 8, 144, 64], [1, 2, 4, 8, 24, 192], [1, 2, 4, 8, 16, 64], [161, 130, 12, 8, 16, 64], [9, 2, 132, 8, 16, 64]], 'inner_hash': 51, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': False, 'inner_tex': 'C_2^5', 'inner_used': [1, 2, 3, 5, 6], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 12]], 'label': '256.29702', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^5:C2^3', 'ngens': 5, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 52, 'number_divisions': 52, 'number_normal_subgroups': 455, 'number_subgroup_autclasses': 304, 'number_subgroup_classes': 2085, 'number_subgroups': 6079, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 95], [4, 160]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 8, 'outer_gen_orders': [4, 4, 8, 4, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[13, 10, 36, 136, 80, 96], [137, 130, 14, 8, 212, 226], [39, 34, 174, 136, 54, 98], [37, 2, 36, 136, 216, 72], [41, 138, 4, 8, 184, 104], [13, 2, 164, 136, 112, 104]], 'outer_group': None, 'outer_hash': 5400958556047536679, 'outer_nilpotent': True, 'outer_order': 8192, 'outer_permdeg': 128, 'outer_perms': [3133172676045219348285825851773905836753429280809019671862764380047402381809674494068230792255091047520648782297897630841647963171537941539804064372121692061934673899443868789777485406563271143412269512279950358132, 142353231899718321420531998981040015141880251927388122177754788290338727740457034442323425696258982947596301288113373415572622660670175106470988847480225980951034439123947326669376989302088589959479311764017305784, 6193467463556332895888554163778136610461405672938045056402913864758973659875429770428243063626250085174118773764657483540371219401934896285722290835415995584352024582841408659066273576680051233893011006024320843314, 9230039001436846499163838454276804861751279272256206078601679122931602160265704111403861960619325818473684287430026903410268454051470831822788153719825031570202563144649103770154646229164804114056118807028835124239, 12266610259063515524221406722297093328170319545366209670337422126616185221701370795418752422770911331602051185454742436713606327867009848694076967523106952986272923496449026553336260228831277278458006584750259694010, 15303182063274058074616621575878722010385450110814984313220911819622988795873732852889713368712503976718187596539720169434122452229644568005464391469515884263050400106536101928006762409042962760502612281569888025711], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6.C_2^5.C_2^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 20, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 8], [4, 12]], 'representations': {'PC': {'code': 10276026275316907127149648, 'gens': [1, 2, 3, 4, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 7044, 2892, 260, 116, 4038, 2710, 166]}, 'Perm': {'d': 20, 'gens': [135936679847638918, 262581193678014743, 123134628699895680, 122398327071824341, 392327162440029496, 392327162440036537, 392327162527104000, 392327162440012800]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5:C_2^3', 'transitive_degree': 32, '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: 102015068
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 29702, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 102015079
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 29702, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
  • id: 102015090
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 29702, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
  • id: 102015101
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 29702, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 160, 'size': 1}
  • id: 102015112
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 29702, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 40, 'size': 1}
  • id: 102015116
    {'aut_label': '2E', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 29702, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 136, 'size': 1}
  • id: 102015117
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 7, 'group_counter': 29702, 'group_order': 256, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 168, 'size': 1}
  • id: 102015118
    {'aut_label': '2E', 'centralizer': '1.a1', 'counter': 8, 'group_counter': 29702, 'group_order': 256, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 8, 'size': 1}
  • id: 102015119
    {'aut_label': '2H', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 29702, 'group_order': 256, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 2, 'size': 2}
  • id: 102015069
    {'aut_label': '2H', 'centralizer': '2.a1', 'counter': 10, 'group_counter': 29702, 'group_order': 256, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 34, 'size': 2}
  • id: 102015070
    {'aut_label': '2H', 'centralizer': '2.a1', 'counter': 11, 'group_counter': 29702, 'group_order': 256, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 10, 'size': 2}
  • id: 102015071
    {'aut_label': '2H', 'centralizer': '2.a1', 'counter': 12, 'group_counter': 29702, 'group_order': 256, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 42, 'size': 2}
  • id: 102015072
    {'aut_label': '2L', 'centralizer': '4.a1', 'counter': 13, 'group_counter': 29702, 'group_order': 256, 'label': '2L', 'order': 2, 'powers': [1], 'representative': 4, 'size': 4}
  • id: 102015073
    {'aut_label': '2M', 'centralizer': '4.a1', 'counter': 14, 'group_counter': 29702, 'group_order': 256, 'label': '2M', 'order': 2, 'powers': [1], 'representative': 1, 'size': 4}
  • id: 102015074
    {'aut_label': '2N', 'centralizer': '4.j1', 'counter': 15, 'group_counter': 29702, 'group_order': 256, 'label': '2N', 'order': 2, 'powers': [1], 'representative': 68, 'size': 4}
  • id: 102015075
    {'aut_label': '2L', 'centralizer': '4.a1', 'counter': 16, 'group_counter': 29702, 'group_order': 256, 'label': '2O', 'order': 2, 'powers': [1], 'representative': 36, 'size': 4}
  • id: 102015076
    {'aut_label': '2L', 'centralizer': '4.a1', 'counter': 17, 'group_counter': 29702, 'group_order': 256, 'label': '2P', 'order': 2, 'powers': [1], 'representative': 6, 'size': 4}
  • id: 102015077
    {'aut_label': '2M', 'centralizer': '4.a1', 'counter': 18, 'group_counter': 29702, 'group_order': 256, 'label': '2Q', 'order': 2, 'powers': [1], 'representative': 129, 'size': 4}
  • id: 102015078
    {'aut_label': '2M', 'centralizer': '4.a1', 'counter': 19, 'group_counter': 29702, 'group_order': 256, 'label': '2R', 'order': 2, 'powers': [1], 'representative': 5, 'size': 4}
  • id: 102015080
    {'aut_label': '2M', 'centralizer': '4.a1', 'counter': 20, 'group_counter': 29702, 'group_order': 256, 'label': '2S', 'order': 2, 'powers': [1], 'representative': 3, 'size': 4}
  • id: 102015081
    {'aut_label': '2N', 'centralizer': '4.j1', 'counter': 21, 'group_counter': 29702, 'group_order': 256, 'label': '2T', 'order': 2, 'powers': [1], 'representative': 100, 'size': 4}
  • id: 102015082
    {'aut_label': '2U', 'centralizer': '4.l1', 'counter': 22, 'group_counter': 29702, 'group_order': 256, 'label': '2U', 'order': 2, 'powers': [1], 'representative': 70, 'size': 4}
  • id: 102015083
    {'aut_label': '2L', 'centralizer': '4.a1', 'counter': 23, 'group_counter': 29702, 'group_order': 256, 'label': '2V', 'order': 2, 'powers': [1], 'representative': 38, 'size': 4}
  • id: 102015084
    {'aut_label': '2M', 'centralizer': '4.a1', 'counter': 24, 'group_counter': 29702, 'group_order': 256, 'label': '2W', 'order': 2, 'powers': [1], 'representative': 133, 'size': 4}
  • id: 102015085
    {'aut_label': '2M', 'centralizer': '4.a1', 'counter': 25, 'group_counter': 29702, 'group_order': 256, 'label': '2X', 'order': 2, 'powers': [1], 'representative': 131, 'size': 4}
  • id: 102015086
    {'aut_label': '2M', 'centralizer': '4.a1', 'counter': 26, 'group_counter': 29702, 'group_order': 256, 'label': '2Y', 'order': 2, 'powers': [1], 'representative': 7, 'size': 4}
  • id: 102015087
    {'aut_label': '2U', 'centralizer': '4.l1', 'counter': 27, 'group_counter': 29702, 'group_order': 256, 'label': '2Z', 'order': 2, 'powers': [1], 'representative': 102, 'size': 4}
  • id: 102015088
    {'aut_label': '2M', 'centralizer': '4.a1', 'counter': 28, 'group_counter': 29702, 'group_order': 256, 'label': '2AA', 'order': 2, 'powers': [1], 'representative': 135, 'size': 4}
  • id: 102015089
    {'aut_label': '2AB', 'centralizer': '8.v1', 'counter': 29, 'group_counter': 29702, 'group_order': 256, 'label': '2AB', 'order': 2, 'powers': [1], 'representative': 19, 'size': 8}
  • id: 102015091
    {'aut_label': '2AB', 'centralizer': '8.v1', 'counter': 30, 'group_counter': 29702, 'group_order': 256, 'label': '2AC', 'order': 2, 'powers': [1], 'representative': 87, 'size': 8}
  • id: 102015092
    {'aut_label': '4A', 'centralizer': '4.o1', 'counter': 31, 'group_counter': 29702, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 64, 'size': 4}
  • id: 102015093
    {'aut_label': '4A', 'centralizer': '4.o1', 'counter': 32, 'group_counter': 29702, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 96, 'size': 4}
  • id: 102015094
    {'aut_label': '4A', 'centralizer': '4.o1', 'counter': 33, 'group_counter': 29702, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 66, 'size': 4}
  • id: 102015095
    {'aut_label': '4A', 'centralizer': '4.o1', 'counter': 34, 'group_counter': 29702, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 98, 'size': 4}
  • id: 102015096
    {'aut_label': '4E', 'centralizer': '8.be2', 'counter': 35, 'group_counter': 29702, 'group_order': 256, 'label': '4E', 'order': 4, 'powers': [3], 'representative': 16, 'size': 8}
  • id: 102015097
    {'aut_label': '4E', 'centralizer': '8.be2', 'counter': 36, 'group_counter': 29702, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [4], 'representative': 80, 'size': 8}
  • id: 102015098
    {'aut_label': '4E', 'centralizer': '8.be2', 'counter': 37, 'group_counter': 29702, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [5], 'representative': 20, 'size': 8}
  • id: 102015099
    {'aut_label': '4E', 'centralizer': '8.be2', 'counter': 38, 'group_counter': 29702, 'group_order': 256, 'label': '4H', 'order': 4, 'powers': [4], 'representative': 18, 'size': 8}
  • id: 102015100
    {'aut_label': '4I', 'centralizer': '8.g1', 'counter': 39, 'group_counter': 29702, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [6], 'representative': 65, 'size': 8}
  • id: 102015102
    {'aut_label': '4J', 'centralizer': '8.x1', 'counter': 40, 'group_counter': 29702, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [2], 'representative': 17, 'size': 8}
  • id: 102015103
    {'aut_label': '4E', 'centralizer': '8.be2', 'counter': 41, 'group_counter': 29702, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [5], 'representative': 84, 'size': 8}
  • id: 102015104
    {'aut_label': '4E', 'centralizer': '8.be2', 'counter': 42, 'group_counter': 29702, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [3], 'representative': 82, 'size': 8}
  • id: 102015105
    {'aut_label': '4E', 'centralizer': '8.be2', 'counter': 43, 'group_counter': 29702, 'group_order': 256, 'label': '4M', 'order': 4, 'powers': [7], 'representative': 22, 'size': 8}
  • id: 102015106
    {'aut_label': '4N', 'centralizer': '8.bb1', 'counter': 44, 'group_counter': 29702, 'group_order': 256, 'label': '4N', 'order': 4, 'powers': [8], 'representative': 81, 'size': 8}
  • id: 102015107
    {'aut_label': '4I', 'centralizer': '8.g1', 'counter': 45, 'group_counter': 29702, 'group_order': 256, 'label': '4O', 'order': 4, 'powers': [8], 'representative': 69, 'size': 8}
  • id: 102015108
    {'aut_label': '4N', 'centralizer': '8.bb1', 'counter': 46, 'group_counter': 29702, 'group_order': 256, 'label': '4P', 'order': 4, 'powers': [6], 'representative': 21, 'size': 8}
  • id: 102015109
    {'aut_label': '4I', 'centralizer': '8.g1', 'counter': 47, 'group_counter': 29702, 'group_order': 256, 'label': '4Q', 'order': 4, 'powers': [6], 'representative': 67, 'size': 8}
  • id: 102015110
    {'aut_label': '4E', 'centralizer': '8.be2', 'counter': 48, 'group_counter': 29702, 'group_order': 256, 'label': '4R', 'order': 4, 'powers': [7], 'representative': 86, 'size': 8}
  • id: 102015111
    {'aut_label': '4J', 'centralizer': '8.x1', 'counter': 49, 'group_counter': 29702, 'group_order': 256, 'label': '4S', 'order': 4, 'powers': [2], 'representative': 85, 'size': 8}
  • id: 102015113
    {'aut_label': '4N', 'centralizer': '8.bb1', 'counter': 50, 'group_counter': 29702, 'group_order': 256, 'label': '4T', 'order': 4, 'powers': [6], 'representative': 83, 'size': 8}
  • id: 102015114
    {'aut_label': '4I', 'centralizer': '8.g1', 'counter': 51, 'group_counter': 29702, 'group_order': 256, 'label': '4U', 'order': 4, 'powers': [8], 'representative': 71, 'size': 8}
  • id: 102015115
    {'aut_label': '4N', 'centralizer': '8.bb1', 'counter': 52, 'group_counter': 29702, 'group_order': 256, 'label': '4V', 'order': 4, 'powers': [8], 'representative': 23, 'size': 8}
• 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: 1029351
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 1029362
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 1029373
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 1029384
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 1029395
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 1029399
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 1029400
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 1029401
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 1029402
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 1029352
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 1029353
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 1029354
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 1029355
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 1029356
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 1029357
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 1029358
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 1029359
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1q', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 1029360
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1r', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 1029361
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1s', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 1029363
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1t', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 1029364
    {'cdim': 1, 'counter': 21, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1u', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 1029365
    {'cdim': 1, 'counter': 22, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1v', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 1029366
    {'cdim': 1, 'counter': 23, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1w', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 1029367
    {'cdim': 1, 'counter': 24, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1x', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 1029368
    {'cdim': 1, 'counter': 25, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1y', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 1029369
    {'cdim': 1, 'counter': 26, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1z', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 1029370
    {'cdim': 1, 'counter': 27, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1aa', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 1029371
    {'cdim': 1, 'counter': 28, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1ab', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 1029372
    {'cdim': 1, 'counter': 29, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1ac', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 1029374
    {'cdim': 1, 'counter': 30, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1ad', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 1029375
    {'cdim': 1, 'counter': 31, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1ae', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 1029376
    {'cdim': 1, 'counter': 32, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.1af', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 1029377
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, -2, 0, 0, 2, 0, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029378
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 0, 0, -2, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029379
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, 2, -2, -2, -2, 0, 0, 2, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029380
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, 2, -2, 2, 2, 0, 0, -2, 0, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029381
    {'cdim': 2, 'counter': 37, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, -2, -2, -2, -2, 2, 0, 0, -2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029382
    {'cdim': 2, 'counter': 38, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 0, 0, 2, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029383
    {'cdim': 2, 'counter': 39, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, -2, 2, 2, -2, 2, 0, 0, -2, 0, 0, 0, -2, 0, -2, 2, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029385
    {'cdim': 2, 'counter': 40, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 0, 0, 2, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029386
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4a', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029387
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4b', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029388
    {'cdim': 4, 'counter': 43, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4c', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029389
    {'cdim': 4, 'counter': 44, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4d', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029390
    {'cdim': 4, 'counter': 45, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4e', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029391
    {'cdim': 4, 'counter': 46, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4f', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029392
    {'cdim': 4, 'counter': 47, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4g', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029393
    {'cdim': 4, 'counter': 48, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4h', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029394
    {'cdim': 4, 'counter': 49, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4i', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029396
    {'cdim': 4, 'counter': 50, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4j', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029397
    {'cdim': 4, 'counter': 51, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4k', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 1029398
    {'cdim': 4, 'counter': 52, 'faithful': False, 'group': '256.29702', 'group_order': 256, 'image': None, 'label': '256.29702.4l', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• 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: 1421166
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 256, 'label': '256.29702.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 1421185
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 27, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 128, 'label': '256.29702.1aa', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 1421186
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 28, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.29702.1ab', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 1421187
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 29, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.29702.1ac', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 1421189
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 30, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 128, 'label': '256.29702.1ad', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 1421190
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 31, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.29702.1ae', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 1421191
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 32, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.29702.1af', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 1421177
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1', 'kernel_order': 128, 'label': '256.29702.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 1421188
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1', 'kernel_order': 128, 'label': '256.29702.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 1421199
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1', 'kernel_order': 128, 'label': '256.29702.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 1421210
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1', 'kernel_order': 128, 'label': '256.29702.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 1421214
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1', 'kernel_order': 128, 'label': '256.29702.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 1421215
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1', 'kernel_order': 128, 'label': '256.29702.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 1421216
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1', 'kernel_order': 128, 'label': '256.29702.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 1421217
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1', 'kernel_order': 128, 'label': '256.29702.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 1421167
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1', 'kernel_order': 128, 'label': '256.29702.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 1421168
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1', 'kernel_order': 128, 'label': '256.29702.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 1421169
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1', 'kernel_order': 128, 'label': '256.29702.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 1421170
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1', 'kernel_order': 128, 'label': '256.29702.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 1421171
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1', 'kernel_order': 128, 'label': '256.29702.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 1421172
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1', 'kernel_order': 128, 'label': '256.29702.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 1421173
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1', 'kernel_order': 128, 'label': '256.29702.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 1421174
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 17, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1', 'kernel_order': 128, 'label': '256.29702.1q', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 1421175
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 18, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1', 'kernel_order': 128, 'label': '256.29702.1r', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 1421176
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 19, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1', 'kernel_order': 128, 'label': '256.29702.1s', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 1421178
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 20, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1', 'kernel_order': 128, 'label': '256.29702.1t', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 1421179
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 21, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1', 'kernel_order': 128, 'label': '256.29702.1u', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 1421180
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 22, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 128, 'label': '256.29702.1v', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 1421181
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 23, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.29702.1w', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 1421182
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 24, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 128, 'label': '256.29702.1x', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 1421183
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 25, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.29702.1y', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 1421184
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 26, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 128, 'label': '256.29702.1z', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 1421192
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 33, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.bi1', 'kernel_order': 32, 'label': '256.29702.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421193
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 34, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.bi1', 'kernel_order': 32, 'label': '256.29702.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421194
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 35, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.bi1', 'kernel_order': 32, 'label': '256.29702.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421195
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 36, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.bi1', 'kernel_order': 32, 'label': '256.29702.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421196
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 37, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.bi1', 'kernel_order': 32, 'label': '256.29702.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421197
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 38, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.bi1', 'kernel_order': 32, 'label': '256.29702.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421198
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 39, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.bi1', 'kernel_order': 32, 'label': '256.29702.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421200
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 40, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.bi1', 'kernel_order': 32, 'label': '256.29702.2h', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421201
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 41, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1', 'kernel_order': 8, 'label': '256.29702.4a', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421202
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 42, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1', 'kernel_order': 8, 'label': '256.29702.4b', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421203
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1', 'kernel_order': 8, 'label': '256.29702.4c', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421204
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 44, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1', 'kernel_order': 8, 'label': '256.29702.4d', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421205
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1', 'kernel_order': 8, 'label': '256.29702.4e', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421206
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1', 'kernel_order': 8, 'label': '256.29702.4f', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421207
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 47, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1', 'kernel_order': 8, 'label': '256.29702.4g', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 1421208
    {'center': '16.c1', 'center_index': 16, 'center_order': 16, 'counter': 48, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1', 'kernel_order': 8, 'label': '256.29702.4h', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 1421209
    {'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 49, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.29702.4i', 'nt': [8, 22], '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]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421211
    {'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 50, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.29702.4j', 'nt': [8, 22], '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]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421212
    {'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 51, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.29702.4k', 'nt': [8, 22], '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]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 1421213
    {'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 52, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.29702', 'group_counter': 29702, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.29702.4l', 'nt': [8, 22], '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]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 30063313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.29702.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.29702', 'subgroup_hash': 29702, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 2}
  • id: 30063424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': True, '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: 30063535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2177', 'subgroup_hash': 2177, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1041', 'subgroup_hash': 1041, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1354', 'subgroup_hash': 1354, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1135', 'subgroup_hash': 1135, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1137', 'subgroup_hash': 1137, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.h1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1143', 'subgroup_hash': 1143, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.i1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1411', 'subgroup_hash': 1411, 'subgroup_order': 128, 'subgroup_tex': 'C_2.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.j1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1429', 'subgroup_hash': 1429, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.2.k1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1410', 'subgroup_hash': 1410, 'subgroup_order': 128, 'subgroup_tex': 'C_2.D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 30063358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.205', 'subgroup_hash': 205, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.195', 'subgroup_hash': 195, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.71', 'subgroup_hash': 71, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.205', 'subgroup_hash': 205, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.203', 'subgroup_hash': 203, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.71', 'subgroup_hash': 71, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.73', 'subgroup_hash': 73, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.bf2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.205', 'subgroup_hash': 205, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.bg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.71', 'subgroup_hash': 71, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 30063561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.4.bh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.4.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.4.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 30063566
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 32, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 30063567
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 30063568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 32, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 30063575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.u2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.u2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063589
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 30063590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063591
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.be2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.be2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.bh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.8.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 30063608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 30063613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 30063324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.8.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063329
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063330
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063331
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063337
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063338
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063339
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 122, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063340
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063341
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 124, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063342
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 125, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063343
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 127, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 128, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.16.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063348
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063349
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063351
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063354
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.w2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w2', 'outer_equivalence': True, 'perfect': False, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.x2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x2', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.y2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y2', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063362
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063363
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063366
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.be2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be2', 'outer_equivalence': True, 'perfect': False, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063367
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063372
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063384
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063387
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063390
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063392
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063393
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063394
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cc2', 'outer_equivalence': True, 'perfect': False, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063395
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063397
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063398
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cf2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf2', 'outer_equivalence': True, 'perfect': False, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.ci2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ci2', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cj2', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.ck2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ck2', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cl2', 'outer_equivalence': True, 'perfect': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063410
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063417
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 30063418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.16.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063419
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 195, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063420
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 196, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.51', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'D', 'Phi', 'S', 'U1', 'L1', 'D1', 'C5'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063421
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 197, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063422
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 198, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063423
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 199, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 200, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063427
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 201, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063428
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063429
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.i2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i2', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063431
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063432
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063433
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n2', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063439
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063440
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063442
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063443
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063444
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063446
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063448
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063450
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063451
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063459
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063460
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063461
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063462
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj2', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063463
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bj3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj3', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063466
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063467
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bo2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo2', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063472
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs2', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063476
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bt2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt2', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063482
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bw2', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063485
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.32.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 30063493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 261, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 262, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.261', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 261, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 263, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.215', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 215, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 264, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29702.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063499
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063503
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 270, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.64.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063504
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 271, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.64.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063505
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063506
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063507
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.m2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.m2', 'outer_equivalence': True, 'perfect': False, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063509
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.n2', 'outer_equivalence': True, 'perfect': False, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063510
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063511
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063512
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063514
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 280, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.64.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063515
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063516
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063517
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063518
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.u2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.u2', 'outer_equivalence': True, 'perfect': False, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063519
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063520
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063521
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063522
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 288, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.64.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063523
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 289, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.64.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 30063525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063526
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063527
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063528
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063529
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.29702.64.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 30063530
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 295, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.29702.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.2177', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2177, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4:D_4', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063531
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 296, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.29702.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.2264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2:C_2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063532
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 297, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.29702.128.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.2216', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2216, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2:C_2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063533
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.128.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063534
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.128.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063537
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.128.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063538
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.128.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063539
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.128.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063540
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 303, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.29702.128.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 30063541
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.29702', 'ambient_counter': 29702, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 304, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.29702.256.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '256.29702', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29702, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5:C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 30063465
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.bb1', '16.cm1'], 'contains': ['64.o1', '64.q1', '64.be1'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [5686, -1, 5671, -1], 'generators': [19, 196, 32], 'label': '256.29702.32.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.v1', 'old_label': '32.bl1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063506
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.i1', '32.bg1', '32.bj1', '32.bj2', '32.bn1'], 'contains': ['128.b1', '128.e1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [1798, -1, 1793, -1], 'generators': [6, 32], 'label': '256.29702.64.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.m1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063507
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.m2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.i2', '32.bg1', '32.bj3', '32.bn1'], 'contains': ['128.b1', '128.e1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [2009, -1, 2004, -1], 'generators': [6, 40], 'label': '256.29702.64.m2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.m2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063441
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '16.bg1', '16.bk1', '16.bq1', '16.bt1', '16.bv1'], 'contains': ['64.b1', '64.i1', '64.x1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8831, -1, 8807, -1], 'generators': [19, 8, 128], 'label': '256.29702.32.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.r1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063442
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.i1', '16.bh1', '16.bl1', '16.bn1', '16.bo1', '16.bp1'], 'contains': ['64.b1', '64.y1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [4993, -1, 4979, -1], 'generators': [65, 128], 'label': '256.29702.32.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.s1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063401
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.ci1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.p1', '8.cc1'], 'contains': ['32.bo2', '32.bp1', '32.bt1', '32.cb1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [3262, -1, 3252, -1], 'generators': [1, 196, 32], 'label': '256.29702.16.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.ci1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ci1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063440
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '16.bf1', '16.bj1', '16.bn1', '16.bo1', '16.bp1'], 'contains': ['64.b1', '64.f1', '64.u1', '64.u2'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3966, -1, 3955, -1], 'generators': [1, 8, 128], 'label': '256.29702.32.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.q1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063313
    {'ambient': '256.29702', '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': '32.b1', 'complements': ['256.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1', '2.h1', '2.i1', '2.j1', '2.k1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3347, 6388, 3332, 6384], 'generators': [1, 2, 4, 64, 16], 'label': '256.29702.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1', '2.h1', '2.i1', '2.j1', '2.k1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '32.51', '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': '32.51'}
  • id: 30063314
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.i1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 32, 'centralizer': '32.b1', 'complements': ['128.d1', '128.f1', '128.e1', '128.h1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.q1', '4.s1', '4.u1', '4.v1', '4.z1', '4.bb1', '4.bd1', '4.bg1', '4.bg2'], 'core': '2.i1', 'coset_action_label': None, 'count': 4, 'diagramx': [2958, 2976, 2959, 2975], 'generators': [1, 18, 4, 64], 'label': '256.29702.2.i1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.i1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.q1', '4.s1', '4.u1', '4.v1', '4.z1', '4.bb1', '4.bd1', '4.bg1', '4.bg2'], 'normalizer': '1.a1', 'old_label': '2.i1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.i1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063315
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.bt1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.j1', '4.bj1'], 'contains': ['16.m1', '16.bg1', '16.bq1', '16.br1', '16.bt1', '16.bz1'], 'core': '16.m1', 'coset_action_label': None, 'count': 8, 'diagramx': [9923, -1, 9895, -1], 'generators': [17, 2, 196, 8], 'label': '256.29702.8.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bt1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063316
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.bu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.l1', '4.bj1'], 'contains': ['16.m1', '16.bi1', '16.bs1', '16.bu1'], 'core': '16.m1', 'coset_action_label': None, 'count': 8, 'diagramx': [8857, -1, 8832, -1], 'generators': [21, 2, 196], 'label': '256.29702.8.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bu1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063317
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.bv1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.m1', '4.bj1'], 'contains': ['16.n1', '16.bg1', '16.bi1', '16.bv1', '16.bw1'], 'core': '16.n1', 'coset_action_label': None, 'count': 16, 'diagramx': [9534, -1, 9508, -1], 'generators': [17, 2, 64], 'label': '256.29702.8.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bv1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bv1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063318
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.bw1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.q1', '4.bi1'], 'contains': ['16.o1', '16.bj1', '16.bl1', '16.bn1', '16.bp1'], 'core': '16.o1', 'coset_action_label': None, 'count': 32, 'diagramx': [5280, -1, 5266, -1], 'generators': [1, 6, 196], 'label': '256.29702.8.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bw1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063319
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.bx1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.r1', '4.bi1'], 'contains': ['16.p1', '16.bj1', '16.bl1', '16.bo1', '16.bp1'], 'core': '16.p1', 'coset_action_label': None, 'count': 32, 'diagramx': [5101, -1, 5086, -1], 'generators': [1, 6, 64], 'label': '256.29702.8.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bx1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063320
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.by1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.u1', '4.bj1'], 'contains': ['16.o1', '16.bk1', '16.bq1', '16.bs1', '16.bv1'], 'core': '16.o1', 'coset_action_label': None, 'count': 16, 'diagramx': [9342, -1, 9316, -1], 'generators': [21, 6, 196], 'label': '256.29702.8.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.u1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.by1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.by1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063321
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.bz1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.w1', '4.bj1'], 'contains': ['16.o1', '16.bm1', '16.br1', '16.bs1', '16.bw1'], 'core': '16.o1', 'coset_action_label': None, 'count': 16, 'diagramx': [9739, -1, 9712, -1], 'generators': [17, 6, 196], 'label': '256.29702.8.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.w1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bz1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bz1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063322
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.ca1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.x1', '4.bj1'], 'contains': ['16.p1', '16.bk1', '16.bm1', '16.bt1', '16.bu1', '16.bv1', '16.bw1'], 'core': '16.p1', 'coset_action_label': None, 'count': 32, 'diagramx': [9193, -1, 9167, -1], 'generators': [17, 6, 64], 'label': '256.29702.8.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.ca1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ca1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063323
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.cb1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.a1'], 'contains': ['16.ca1', '16.cb1', '16.cc1', '16.cc2', '16.cf1', '16.cf2', '16.cs1'], 'core': '32.h1', 'coset_action_label': None, 'count': 32, 'diagramx': [34, -1, 33, -1], 'generators': [1, 2, 4, 160, 136], 'label': '256.29702.8.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '8.cb1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063324
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.cc1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.f1'], 'contains': ['16.cc2', '16.cd1', '16.ce1', '16.ci1', '16.ci2', '16.cj1', '16.cj2', '16.ct1'], 'core': '32.h1', 'coset_action_label': None, 'count': 32, 'diagramx': [2563, -1, 2557, -1], 'generators': [1, 2, 196, 32], 'label': '256.29702.8.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '8.cc1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063325
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.j1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 32, 'centralizer': '32.b1', 'complements': ['128.f1', '128.d1', '128.i1', '128.e1', '128.h1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.q1', '4.t1', '4.v1', '4.w1', '4.ba1', '4.bc1', '4.bd1', '4.bh1', '4.bh2'], 'core': '2.j1', 'coset_action_label': None, 'count': 4, 'diagramx': [3486, 1820, 3470, 1820], 'generators': [17, 18, 4, 64], 'label': '256.29702.2.j1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.q1', '4.t1', '4.v1', '4.w1', '4.ba1', '4.bc1', '4.bd1', '4.bh1', '4.bh2'], 'normalizer': '1.a1', 'old_label': '2.j1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.j1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063326
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.cd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.s1'], 'contains': ['16.cf2', '16.cg1', '16.ch1', '16.ck1', '16.ck2', '16.cl1', '16.cl2'], 'core': '32.h1', 'coset_action_label': None, 'count': 64, 'diagramx': [165, -1, 165, -1], 'generators': [1, 6, 80], 'label': '256.29702.8.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1', 'old_label': '8.cd1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063327
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.ce1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.bb1'], 'contains': ['16.ci2', '16.ck2', '16.cm1', '16.cn1', '16.cq1'], 'core': '32.h1', 'coset_action_label': None, 'count': 32, 'diagramx': [1356, -1, 1352, -1], 'generators': [1, 18, 196], 'label': '256.29702.8.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1', 'old_label': '8.ce1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ce1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063328
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.cf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.bf2'], 'contains': ['16.cj2', '16.cl2', '16.co1', '16.cp1', '16.cr1'], 'core': '32.h1', 'coset_action_label': None, 'count': 32, 'diagramx': [1001, -1, 998, -1], 'generators': [21, 18, 212], 'label': '256.29702.8.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bf2', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bf2', 'old_label': '8.cf1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063329
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.a1', 'aut_quo_index': 5040, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1', '8.h1'], 'contains': ['32.a1', '32.b1', '32.c1', '32.bm1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5772, 7807, 5755, 7803], 'generators': [2, 8, 160, 128], 'label': '256.29702.16.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1', '8.h1'], 'normal_contains': ['32.a1', '32.b1', '32.c1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063330
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.b1', 'aut_quo_index': 5040, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.i1', '8.j1', '8.k1', '8.l1', '8.m1', '8.n1', '8.o1'], 'contains': ['32.b1', '32.d1', '32.i1', '32.i2', '32.bn1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5439, 6073, 5423, 6071], 'generators': [6, 8, 160, 128], 'label': '256.29702.16.b1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.i1', '8.j1', '8.k1', '8.l1', '8.m1', '8.n1', '8.o1'], 'normal_contains': ['32.b1', '32.d1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063331
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.c1', 'aut_quo_index': 10080, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16384, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.i1', '8.p1', '8.q1', '8.r1', '8.s1', '8.t1', '8.u1', '8.u2'], 'contains': ['32.b1', '32.h1', '32.j1', '32.q1', '32.bo1', '32.bo2'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1831, 2943, 1827, 2943], 'generators': [1, 8, 160, 128], 'label': '256.29702.16.c1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.c1', 'normal_contained_in': ['8.b1', '8.i1', '8.p1', '8.q1', '8.r1', '8.s1', '8.t1', '8.u1', '8.u2'], 'normal_contains': ['32.b1', '32.h1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063332
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.d1', 'aut_quo_index': 2520, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '4.j1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.j1', '8.p1', '8.v1', '8.w1', '8.x1', '8.y1'], 'contains': ['32.b1', '32.e1', '32.k1', '32.bp1'], 'core': '16.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6274, 5951, 6256, 5949], 'generators': [196, 8, 160, 128], 'label': '256.29702.16.d1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.d1', 'normal_contained_in': ['8.c1', '8.j1', '8.p1', '8.v1', '8.w1', '8.x1', '8.y1'], 'normal_contains': ['32.b1', '32.e1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063333
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.e1', 'aut_quo_index': 2520, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '4.l1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.k1', '8.q1', '8.z1', '8.ba1', '8.bb1'], 'contains': ['32.b1', '32.f1', '32.l1', '32.bq1'], 'core': '16.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5856, 6194, 5840, 6193], 'generators': [198, 8, 160, 128], 'label': '256.29702.16.e1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.e1', 'normal_contained_in': ['8.c1', '8.k1', '8.q1', '8.z1', '8.ba1', '8.bb1'], 'normal_contains': ['32.b1', '32.f1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063334
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.f1', 'aut_quo_index': 5040, 'aut_stab_index': 2, 'aut_weyl_group': '32.6', 'aut_weyl_index': 8192, 'centralizer': '8.v1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '8.l1', '8.r1', '8.v1', '8.z1', '8.bc1', '8.bd1'], 'contains': ['32.b1', '32.m1', '32.r1', '32.br1'], 'core': '16.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [5941, 5595, 5924, 5593], 'generators': [19, 8, 160, 128], 'label': '256.29702.16.f1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.f1', 'normal_contained_in': ['8.d1', '8.l1', '8.r1', '8.v1', '8.z1', '8.bc1', '8.bd1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.f1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063335
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.g1', 'aut_quo_index': 5040, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 8192, 'centralizer': '4.o1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.j1', '8.k1', '8.s1', '8.bc1', '8.be1', '8.be2', '8.bf1'], 'contains': ['32.b1', '32.g1', '32.n1', '32.n2'], 'core': '16.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [6065, 5773, 6048, 5771], 'generators': [64, 8, 160], 'label': '256.29702.16.g1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.g1', 'normal_contained_in': ['8.e1', '8.j1', '8.k1', '8.s1', '8.bc1', '8.be1', '8.be2', '8.bf1'], 'normal_contains': ['32.b1', '32.g1'], 'normalizer': '1.a1', 'old_label': '16.g1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063336
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.k1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 64, 'centralizer': '32.b1', 'complements': ['128.g1', '128.i1', '128.d1', '128.f1', '128.e1'], 'conjugacy_class_count': 8, 'contained_in': ['1.a1'], 'contains': ['4.r1', '4.s1', '4.t1', '4.x1', '4.y1', '4.z1', '4.ba1', '4.be1', '4.bf1', '4.bf2', '4.bg1', '4.bg2', '4.bh1', '4.bh2'], 'core': '2.k1', 'coset_action_label': None, 'count': 8, 'diagramx': [2681, 2232, 2682, 2231], 'generators': [1, 18, 4, 80], 'label': '256.29702.2.k1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.r1', '4.s1', '4.t1', '4.x1', '4.y1', '4.z1', '4.ba1', '4.be1', '4.bf1', '4.bf2', '4.bg1', '4.bg2', '4.bh1', '4.bh2'], 'normalizer': '1.a1', 'old_label': '2.k1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.k1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063337
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.h1', 'aut_quo_index': 20160, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 32768, 'centralizer': '8.be2', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['8.f1', '8.m1', '8.r1', '8.t1', '8.u1', '8.u2', '8.w1', '8.ba1', '8.bd1', '8.be1', '8.be2', '8.bg1', '8.bh1', '8.bh2'], 'contains': ['32.b1', '32.o1', '32.bs1', '32.bs2'], 'core': '16.h1', 'coset_action_label': None, 'count': 8, 'diagramx': [2968, 2159, 2960, 2158], 'generators': [80, 8, 128], 'label': '256.29702.16.h1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.h1', 'normal_contained_in': ['8.f1', '8.m1', '8.r1', '8.t1', '8.u1', '8.u2', '8.w1', '8.ba1', '8.bd1', '8.be1', '8.be2', '8.bg1', '8.bh1', '8.bh2'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.h1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063338
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.i1', 'aut_quo_index': 10080, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16384, 'centralizer': '8.g1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.n1', '8.p1', '8.q1', '8.s1', '8.bd1', '8.bg1', '8.bh1', '8.bh2'], 'contains': ['32.b1', '32.s1', '32.bt1', '32.bt2'], 'core': '16.i1', 'coset_action_label': None, 'count': 4, 'diagramx': [4025, 3122, 4014, 3121], 'generators': [65, 160, 128], 'label': '256.29702.16.i1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.i1', 'normal_contained_in': ['8.g1', '8.n1', '8.p1', '8.q1', '8.s1', '8.bd1', '8.bg1', '8.bh1', '8.bh2'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.i1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063464
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '32.bk1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.z1', '16.ck1', '16.ck2'], 'contains': ['64.n1', '64.q1', '64.r1'], 'core': '128.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [2047, -1, 2041, -1], 'generators': [7, 80], 'label': '256.29702.32.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1', 'old_label': '32.bk1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063339
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.j1', 'aut_quo_index': 5040, 'aut_stab_index': 2, 'aut_weyl_group': '32.6', 'aut_weyl_index': 8192, 'centralizer': '8.x1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '8.o1', '8.t1', '8.x1', '8.z1', '8.bf1', '8.bg1'], 'contains': ['32.b1', '32.p1', '32.t1'], 'core': '16.j1', 'coset_action_label': None, 'count': 2, 'diagramx': [6398, 4835, 6380, 4834], 'generators': [17, 8, 160], 'label': '256.29702.16.j1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.j1', 'normal_contained_in': ['8.d1', '8.o1', '8.t1', '8.x1', '8.z1', '8.bf1', '8.bg1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.j1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063340
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '16.k1', 'aut_quo_index': 10080, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16384, 'centralizer': '8.bb1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.h1', '8.l1', '8.o1', '8.u1', '8.u2', '8.y1', '8.bb1', '8.bc1', '8.bf1', '8.bh1', '8.bh2'], 'contains': ['32.b1', '32.u1', '32.bu1'], 'core': '16.k1', 'coset_action_label': None, 'count': 4, 'diagramx': [5648, 5091, 5632, 5079], 'generators': [81, 160, 128], 'label': '256.29702.16.k1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.k1', 'normal_contained_in': ['8.h1', '8.l1', '8.o1', '8.u1', '8.u2', '8.y1', '8.bb1', '8.bc1', '8.bf1', '8.bh1', '8.bh2'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.k1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063341
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.l1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.bi1', '8.bo1', '8.bp1', '8.bq1'], 'contains': ['32.c1', '32.d1', '32.v1', '32.bv1'], 'core': '16.l1', 'coset_action_label': None, 'count': 4, 'diagramx': [6189, 8502, 6172, 8498], 'generators': [2, 4, 8, 128], 'label': '256.29702.16.l1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.l1', 'normal_contained_in': ['8.a1', '8.bi1'], 'normal_contains': ['32.c1', '32.d1'], 'normalizer': '1.a1', 'old_label': '16.l1', 'projective_image': '64.261', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063342
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '16.m1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.c1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '8.bi1', '8.br1', '8.bt1', '8.bu1'], 'contains': ['32.c1', '32.e1', '32.f1', '32.x1', '32.bx1'], 'core': '16.m1', 'coset_action_label': None, 'count': 4, 'diagramx': [8009, 8163, 7987, 8160], 'generators': [2, 196, 8, 128], 'label': '256.29702.16.m1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.m1', 'normal_contained_in': ['8.c1', '8.bi1'], 'normal_contains': ['32.c1', '32.e1', '32.f1'], 'normalizer': '1.a1', 'old_label': '16.m1', 'projective_image': '64.261', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.m1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063343
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.n1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '8.e1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.e1', '8.bi1', '8.bs1', '8.bv1'], 'contains': ['32.c1', '32.g1', '32.z1'], 'core': '16.n1', 'coset_action_label': None, 'count': 4, 'diagramx': [7885, 7985, 7863, 7981], 'generators': [2, 64, 8], 'label': '256.29702.16.n1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.n1', 'normal_contained_in': ['8.e1', '8.bi1'], 'normal_contains': ['32.c1', '32.g1'], 'normalizer': '1.a1', 'old_label': '16.n1', 'projective_image': '64.261', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.n1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063344
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.o1', 'aut_quo_index': 4, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['8.j1', '8.bi1', '8.bw1', '8.by1', '8.bz1'], 'contains': ['32.d1', '32.e1', '32.g1', '32.bb1'], 'core': '16.o1', 'coset_action_label': None, 'count': 8, 'diagramx': [8589, 6717, 8565, 6713], 'generators': [6, 196, 8], 'label': '256.29702.16.o1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.o1', 'normal_contained_in': ['8.j1', '8.bi1'], 'normal_contains': ['32.d1', '32.e1', '32.g1'], 'normalizer': '1.a1', 'old_label': '16.o1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063345
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.p1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['8.k1', '8.bi1', '8.bx1', '8.ca1'], 'contains': ['32.d1', '32.f1', '32.g1', '32.bc1'], 'core': '16.p1', 'coset_action_label': None, 'count': 8, 'diagramx': [7733, 6934, 7712, 6933], 'generators': [6, 64, 8], 'label': '256.29702.16.p1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.p1', 'normal_contained_in': ['8.k1', '8.bi1'], 'normal_contains': ['32.d1', '32.f1', '32.g1'], 'normalizer': '1.a1', 'old_label': '16.p1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063346
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.bj1', '8.bk1'], 'contains': ['32.a1', '32.i1', '32.i2', '32.v1', '32.bg1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5523, -1, 5508, -1], 'generators': [2, 4, 160, 128], 'label': '256.29702.16.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.q1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063347
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 64, 'centralizer': '4.a1', 'complements': ['64.be1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.i1', '8.bj1', '8.bo1', '8.cb1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [503, 9408, 500, 9406], 'generators': [1, 2, 4, 160, 8, 128], 'label': '256.29702.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063348
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.b1', '8.bj1', '8.bl1'], 'contains': ['32.a1', '32.j1', '32.w1', '32.bh1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1747, -1, 1742, -1], 'generators': [1, 2, 160, 128], 'label': '256.29702.16.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.r1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063349
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '8.bk1', '8.bm1'], 'contains': ['32.a1', '32.k1', '32.l1', '32.x1', '32.bi1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6968, -1, 6948, -1], 'generators': [2, 196, 160, 128], 'label': '256.29702.16.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.s1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063350
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.d1', '8.bl1', '8.bm1'], 'contains': ['32.a1', '32.m1', '32.p1', '32.y1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7451, -1, 7430, -1], 'generators': [17, 2, 160], 'label': '256.29702.16.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '16.t1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063351
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.e1', '8.bk1', '8.bn1'], 'contains': ['32.a1', '32.n1', '32.n2', '32.z1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6560, -1, 6542, -1], 'generators': [2, 64, 160], 'label': '256.29702.16.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '16.u1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063352
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.g1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.f1', '8.bl1', '8.bn1'], 'contains': ['32.a1', '32.o1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4477, -1, 4465, -1], 'generators': [2, 80], 'label': '256.29702.16.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1', 'old_label': '16.v1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063353
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.i1', '8.bj1'], 'contains': ['32.i1', '32.j1', '32.ba1', '32.bj1', '32.bj2'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [861, -1, 859, -1], 'generators': [1, 6, 160, 128], 'label': '256.29702.16.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.w1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063354
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.w2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.i1', '8.bj1'], 'contains': ['32.i2', '32.j1', '32.ba1', '32.bj3'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1578, -1, 1573, -1], 'generators': [1, 6, 168, 128], 'label': '256.29702.16.w2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.w2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063355
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.j1', '8.bk1'], 'contains': ['32.i1', '32.k1', '32.n1', '32.bb1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7081, -1, 7061, -1], 'generators': [6, 196, 160], 'label': '256.29702.16.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.x1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063356
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.x2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.j1', '8.bk1'], 'contains': ['32.i2', '32.k1', '32.n2', '32.bb1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7223, -1, 7203, -1], 'generators': [6, 196, 168], 'label': '256.29702.16.x2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.x2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063357
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.k1', '8.bk1'], 'contains': ['32.i1', '32.l1', '32.n2', '32.bc1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6713, -1, 6693, -1], 'generators': [6, 64, 160], 'label': '256.29702.16.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.y1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063358
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 64, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.c1', '2.d1'], 'contains': ['8.a1', '8.c1', '8.e1', '8.j1', '8.k1', '8.bi1', '8.bk1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7504, 9899, 7483, 9896], 'generators': [2, 4, 64, 160, 8], 'label': '256.29702.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1', '2.d1'], 'normal_contains': ['8.a1', '8.c1', '8.e1', '8.j1', '8.k1', '8.bi1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063359
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.y2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.k1', '8.bk1'], 'contains': ['32.i2', '32.l1', '32.n1', '32.bc1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6854, -1, 6835, -1], 'generators': [6, 64, 168], 'label': '256.29702.16.y2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.y2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063360
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.r1', '8.bl1'], 'contains': ['32.j1', '32.m1', '32.o1', '32.bk1'], 'core': '64.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2699, -1, 2692, -1], 'generators': [7, 80, 128], 'label': '256.29702.16.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '16.z1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.z1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063361
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.t1', '8.bl1'], 'contains': ['32.j1', '32.o1', '32.p1'], 'core': '64.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3886, -1, 3875, -1], 'generators': [5, 80], 'label': '256.29702.16.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.t1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '16.ba1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ba1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063362
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.v1', '8.bm1'], 'contains': ['32.k1', '32.m1', '32.bd1', '32.bl1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7336, -1, 7316, -1], 'generators': [19, 196, 160, 128], 'label': '256.29702.16.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '16.bb1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063363
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '8.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.x1', '8.bm1'], 'contains': ['32.k1', '32.p1', '32.be1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8134, -1, 8111, -1], 'generators': [17, 196, 160], 'label': '256.29702.16.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '16.bc1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063364
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.z1', '8.bm1'], 'contains': ['32.l1', '32.m1', '32.p1', '32.bf1'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7592, -1, 7571, -1], 'generators': [17, 198, 160], 'label': '256.29702.16.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.z1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '16.bd1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063365
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.be1', '8.bn1'], 'contains': ['32.n1', '32.o1'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4584, -1, 4571, -1], 'generators': [18, 80], 'label': '256.29702.16.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.be1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1', 'old_label': '16.be1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063366
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.be2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.be2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.be2', '8.bn1'], 'contains': ['32.n2', '32.o1'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4674, -1, 4661, -1], 'generators': [18, 64], 'label': '256.29702.16.be2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.be2', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1', 'old_label': '16.be2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063367
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.bo1', '8.br1', '8.bs1'], 'contains': ['32.c1', '32.q1', '32.w1', '32.bw1', '32.bw2'], 'core': '32.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [3460, -1, 3450, -1], 'generators': [1, 2, 8, 128], 'label': '256.29702.16.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bf1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063368
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '8.bp1', '8.bt1', '8.bv1'], 'contains': ['32.c1', '32.r1', '32.t1', '32.y1'], 'core': '32.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [9521, -1, 9495, -1], 'generators': [17, 2, 8], 'label': '256.29702.16.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bg1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063369
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 128, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.c1', '2.e1'], 'contains': ['8.a1', '8.d1', '8.h1', '8.l1', '8.o1', '8.bp1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6268, 8852, 6250, 8849], 'generators': [17, 2, 4, 160], 'label': '256.29702.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.c1', '2.e1'], 'normal_contains': ['8.a1', '8.d1', '8.h1', '8.l1', '8.o1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063370
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.bq1', '8.br1', '8.bs1'], 'contains': ['32.c1', '32.s1', '32.by1'], 'core': '32.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [5198, -1, 5183, -1], 'generators': [65, 2, 128], 'label': '256.29702.16.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bh1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063371
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.h1', '8.bp1', '8.bu1', '8.bv1'], 'contains': ['32.c1', '32.u1'], 'core': '32.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [8719, -1, 8694, -1], 'generators': [81, 2], 'label': '256.29702.16.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bi1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063372
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.i1', '8.bo1', '8.bw1', '8.bx1'], 'contains': ['32.d1', '32.q1', '32.ba1', '32.bz1'], 'core': '32.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [3376, -1, 3366, -1], 'generators': [1, 6, 8, 128], 'label': '256.29702.16.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bj1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063373
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.l1', '8.bp1', '8.by1', '8.ca1'], 'contains': ['32.d1', '32.r1', '32.u1', '32.ca1'], 'core': '32.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [8849, -1, 8824, -1], 'generators': [81, 6, 128], 'label': '256.29702.16.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bk1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063374
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.n1', '8.bq1', '8.bw1', '8.bx1'], 'contains': ['32.d1', '32.s1'], 'core': '32.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [5337, -1, 5322, -1], 'generators': [65, 6], 'label': '256.29702.16.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bl1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063375
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.o1', '8.bp1', '8.bz1', '8.ca1'], 'contains': ['32.d1', '32.t1', '32.u1'], 'core': '32.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [9093, -1, 9069, -1], 'generators': [17, 6], 'label': '256.29702.16.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bm1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063376
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.p1', '8.br1', '8.bw1'], 'contains': ['32.e1', '32.q1', '32.s1', '32.cb1'], 'core': '32.e1', 'coset_action_label': None, 'count': 16, 'diagramx': [4929, -1, 4915, -1], 'generators': [1, 196, 128], 'label': '256.29702.16.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bn1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063377
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.q1', '8.br1', '8.bx1'], 'contains': ['32.f1', '32.q1', '32.s1', '32.cc1'], 'core': '32.f1', 'coset_action_label': None, 'count': 16, 'diagramx': [4787, -1, 4774, -1], 'generators': [1, 198, 128], 'label': '256.29702.16.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bo1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bo1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063378
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.s1', '8.bs1', '8.bw1', '8.bx1'], 'contains': ['32.g1', '32.q1', '32.s1'], 'core': '32.g1', 'coset_action_label': None, 'count': 32, 'diagramx': [5058, -1, 5044, -1], 'generators': [1, 64], 'label': '256.29702.16.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bp1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063379
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.v1', '8.bt1', '8.by1'], 'contains': ['32.e1', '32.r1', '32.bd1', '32.cd1'], 'core': '32.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [9312, -1, 9286, -1], 'generators': [19, 196, 8, 128], 'label': '256.29702.16.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bq1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063380
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 128, 'centralizer': '32.b1', 'complements': ['64.be1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.d1', '2.e1'], 'contains': ['8.a1', '8.f1', '8.m1'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [4550, 8272, 4537, 8269], 'generators': [2, 4, 80], 'label': '256.29702.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.d1', '2.e1'], 'normal_contains': ['8.a1', '8.f1', '8.m1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063381
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '8.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.x1', '8.bt1', '8.bz1'], 'contains': ['32.e1', '32.t1', '32.be1'], 'core': '32.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [9814, -1, 9787, -1], 'generators': [17, 196, 8], 'label': '256.29702.16.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.br1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063382
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.y1', '8.bu1', '8.by1', '8.bz1'], 'contains': ['32.e1', '32.u1'], 'core': '32.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [8977, -1, 8952, -1], 'generators': [21, 196], 'label': '256.29702.16.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.y1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bs1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063383
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.z1', '8.bt1', '8.ca1'], 'contains': ['32.f1', '32.r1', '32.t1', '32.bf1'], 'core': '32.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [9663, -1, 9636, -1], 'generators': [17, 198, 8], 'label': '256.29702.16.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.z1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bt1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063384
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.bb1', '8.bu1', '8.ca1'], 'contains': ['32.f1', '32.u1', '32.ce1'], 'core': '32.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [8438, -1, 8414, -1], 'generators': [21, 198, 128], 'label': '256.29702.16.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bb1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bu1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063385
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.bc1', '8.bv1', '8.by1', '8.ca1'], 'contains': ['32.g1', '32.r1', '32.u1'], 'core': '32.g1', 'coset_action_label': None, 'count': 16, 'diagramx': [9211, -1, 9185, -1], 'generators': [19, 64], 'label': '256.29702.16.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bc1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bv1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063386
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '16.bw1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.bf1', '8.bv1', '8.bz1', '8.ca1'], 'contains': ['32.g1', '32.t1', '32.u1'], 'core': '32.g1', 'coset_action_label': None, 'count': 16, 'diagramx': [9402, -1, 9376, -1], 'generators': [17, 64], 'label': '256.29702.16.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bf1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bw1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bw1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063387
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '16.bx1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '64.138', 'aut_weyl_index': 4096, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.bj1', '8.bo1'], 'contains': ['32.v1', '32.w1', '32.ba1', '32.cf1'], 'core': '64.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [1662, -1, 1658, -1], 'generators': [1, 2, 4, 128], 'label': '256.29702.16.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.bx1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063388
    {'ambient': '256.29702', 'aut_centralizer_order': 256, 'aut_label': '16.by1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16384, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.bi1', '8.bk1'], 'contains': ['32.v1', '32.x1', '32.z1', '32.bb1', '32.bc1'], 'core': '64.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [8285, -1, 8262, -1], 'generators': [2, 4, 64], 'label': '256.29702.16.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bi1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.by1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.by1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063389
    {'ambient': '256.29702', 'aut_centralizer_order': 256, 'aut_label': '16.bz1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16384, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.bm1', '8.bt1'], 'contains': ['32.x1', '32.y1', '32.bd1', '32.be1', '32.bf1'], 'core': '64.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [9966, -1, 9938, -1], 'generators': [17, 2, 196], 'label': '256.29702.16.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '16.bz1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063390
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '16.ca1', 'aut_quo_index': None, 'aut_stab_index': 256, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16384, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['8.bj1', '8.cb1'], 'contains': ['32.bg1', '32.bh1', '32.bj1', '32.bj2', '32.bj3', '32.cf1'], 'core': '128.b1', 'coset_action_label': None, 'count': 256, 'diagramx': [263, -1, 262, -1], 'generators': [1, 2, 4, 32], 'label': '256.29702.16.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.ca1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ca1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063391
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 64, 'centralizer': '16.a1', 'complements': ['64.be1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.e1'], 'contains': ['8.a1', '8.g1', '8.n1', '8.bq1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5514, 9625, 5498, 9623], 'generators': [65, 2, 4, 160], 'label': '256.29702.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1', '2.e1'], 'normal_contains': ['8.a1', '8.g1', '8.n1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063392
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.cb1'], 'contains': ['32.bg1', '32.bm1', '32.bn1', '32.bv1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [1350, -1, 1346, -1], 'generators': [2, 4, 136, 160], 'label': '256.29702.16.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.cb1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063393
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.cb1'], 'contains': ['32.bh1', '32.bm1', '32.bo1', '32.bw1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [517, -1, 515, -1], 'generators': [1, 2, 136, 160], 'label': '256.29702.16.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.cc1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063394
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cc2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.b1', '8.cb1', '8.cc1'], 'contains': ['32.h1', '32.bh1', '32.bm1', '32.bo2', '32.bw2'], 'core': '32.h1', 'coset_action_label': None, 'count': 16, 'diagramx': [1265, -1, 1262, -1], 'generators': [1, 2, 8, 32], 'label': '256.29702.16.cc2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.cc2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cc2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063395
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '8.cc1'], 'contains': ['32.bi1', '32.bm1', '32.bp1', '32.bq1', '32.bx1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [4291, -1, 4279, -1], 'generators': [2, 196, 136, 160], 'label': '256.29702.16.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.cd1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063396
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.ce1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.cc1'], 'contains': ['32.bm1', '32.bt1', '32.bt2', '32.by1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [3584, -1, 3574, -1], 'generators': [65, 2, 160], 'label': '256.29702.16.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.ce1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ce1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063397
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.i1', '8.cb1'], 'contains': ['32.bj1', '32.bj3', '32.bn1', '32.bo1', '32.bo2', '32.bz1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [347, -1, 346, -1], 'generators': [1, 6, 136, 32], 'label': '256.29702.16.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.cf1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063398
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cf2', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.i1', '8.cb1', '8.cd1'], 'contains': ['32.h1', '32.bj2', '32.bj3', '32.bn1', '32.bo1', '32.bz1'], 'core': '32.h1', 'coset_action_label': None, 'count': 32, 'diagramx': [432, -1, 431, -1], 'generators': [1, 6, 136, 160], 'label': '256.29702.16.cf2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.cf2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063399
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.l1', '8.cd1'], 'contains': ['32.bn1', '32.br1', '32.bu1', '32.ca1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [2157, -1, 2151, -1], 'generators': [81, 6, 32], 'label': '256.29702.16.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1', 'old_label': '16.cg1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063400
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.ch1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.m1', '8.cd1'], 'contains': ['32.bn1', '32.bs1', '32.bs2'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [759, -1, 758, -1], 'generators': [6, 80], 'label': '256.29702.16.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1', 'old_label': '16.ch1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ch1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063402
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 128, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.f1', '2.g1'], 'contains': ['8.b1', '8.c1', '8.g1', '8.p1', '8.q1', '8.br1', '8.cc1'], 'core': '4.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [3385, 8070, 3374, 8067], 'generators': [1, 2, 196, 128, 160], 'label': '256.29702.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.a1', '2.f1', '2.g1'], 'normal_contains': ['8.b1', '8.c1', '8.g1', '8.p1', '8.q1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063403
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.ci2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.p1', '8.cc1', '8.ce1'], 'contains': ['32.h1', '32.bp1', '32.bt2', '32.cb1'], 'core': '32.h1', 'coset_action_label': None, 'count': 16, 'diagramx': [2557, -1, 2550, -1], 'generators': [1, 196, 160], 'label': '256.29702.16.ci2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '16.ci2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ci2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063404
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.q1', '8.cc1'], 'contains': ['32.bo2', '32.bq1', '32.bt2', '32.cc1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [3120, -1, 3111, -1], 'generators': [1, 198, 32], 'label': '256.29702.16.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.cj1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063405
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cj2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.q1', '8.cc1', '8.cf1'], 'contains': ['32.h1', '32.bq1', '32.bt1', '32.cc1'], 'core': '32.h1', 'coset_action_label': None, 'count': 16, 'diagramx': [2416, -1, 2409, -1], 'generators': [1, 198, 160], 'label': '256.29702.16.cj2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '16.cj2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cj2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063406
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.ck1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.r1', '8.cd1'], 'contains': ['32.bk1', '32.bo1', '32.br1', '32.bs1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [630, -1, 629, -1], 'generators': [7, 80, 8], 'label': '256.29702.16.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1', 'old_label': '16.ck1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ck1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063407
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.ck2', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.r1', '8.cd1', '8.ce1'], 'contains': ['32.h1', '32.bk1', '32.br1', '32.bs2'], 'core': '32.h1', 'coset_action_label': None, 'count': 32, 'diagramx': [1464, -1, 1460, -1], 'generators': [7, 80, 136], 'label': '256.29702.16.ck2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1', 'old_label': '16.ck2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ck2', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063408
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cl1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.u1', '8.cd1'], 'contains': ['32.bo1', '32.bs2', '32.bu1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [1047, -1, 1044, -1], 'generators': [3, 80], 'label': '256.29702.16.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.u1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1', 'old_label': '16.cl1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063409
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cl2', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['8.u2', '8.cd1', '8.cf1'], 'contains': ['32.h1', '32.bs1', '32.bu1'], 'core': '32.h1', 'coset_action_label': None, 'count': 32, 'diagramx': [1164, -1, 1161, -1], 'generators': [1, 80], 'label': '256.29702.16.cl2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.u2', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1', 'old_label': '16.cl2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cl2', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063410
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.v1', '8.ce1'], 'contains': ['32.bl1', '32.bp1', '32.br1', '32.cd1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [4376, -1, 4364, -1], 'generators': [19, 196, 136, 160], 'label': '256.29702.16.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1', 'old_label': '16.cm1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063411
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.w1', '8.ce1'], 'contains': ['32.bp1', '32.bs2'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [2828, -1, 2820, -1], 'generators': [18, 196], 'label': '256.29702.16.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.w1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1', 'old_label': '16.cn1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063412
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.co1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.ba1', '8.cf1'], 'contains': ['32.bq1', '32.bs1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [2028, -1, 2023, -1], 'generators': [18, 212], 'label': '256.29702.16.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ba1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bf2', 'old_label': '16.co1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.co1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063413
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '2.f1', '2.h1'], 'contains': ['8.b1', '8.d1', '8.f1', '8.r1', '8.t1', '8.bl1'], 'core': '4.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [1448, 6018, 1442, 6016], 'generators': [5, 2, 80, 8], 'label': '256.29702.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.b1', '2.f1', '2.h1'], 'normal_contains': ['8.b1', '8.d1', '8.f1', '8.r1', '8.t1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063414
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.bb1', '8.cf1'], 'contains': ['32.bq1', '32.bu1', '32.ce1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [3746, -1, 3736, -1], 'generators': [21, 198, 160], 'label': '256.29702.16.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bb1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bf2', 'old_label': '16.cp1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063415
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cq1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.bd1', '8.ce1'], 'contains': ['32.br1', '32.bs2', '32.bt2'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [2286, -1, 2280, -1], 'generators': [19, 80], 'label': '256.29702.16.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1', 'old_label': '16.cq1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063416
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '16.cr1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 16384, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.bh2', '8.cf1'], 'contains': ['32.bs1', '32.bt1', '32.bu1'], 'core': '64.d1', 'coset_action_label': None, 'count': 32, 'diagramx': [1922, -1, 1916, -1], 'generators': [23, 80], 'label': '256.29702.16.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bh2', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bf2', 'old_label': '16.cr1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cr1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063417
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '16.cs1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '32.27', 'aut_weyl_index': 8192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['8.bo1', '8.cb1'], 'contains': ['32.bv1', '32.bw1', '32.bw2', '32.bz1', '32.cf1'], 'core': '128.c1', 'coset_action_label': None, 'count': 128, 'diagramx': [946, -1, 943, -1], 'generators': [1, 2, 4, 136], 'label': '256.29702.16.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.cs1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063418
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '16.ct1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '16.11', 'aut_weyl_index': 16384, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['8.br1', '8.cc1'], 'contains': ['32.bw2', '32.bx1', '32.by1', '32.cb1', '32.cc1'], 'core': '128.c1', 'coset_action_label': None, 'count': 128, 'diagramx': [4178, -1, 4166, -1], 'generators': [1, 2, 196], 'label': '256.29702.16.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.ct1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ct1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063419
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.a1', 'aut_quo_index': 36, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '16.q1', '16.r1', '16.s1', '16.t1', '16.u1', '16.v1'], 'contains': ['64.a1', '64.c1', '64.l1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5856, 7423, 5840, 7337], 'generators': [2, 160, 128], 'label': '256.29702.32.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['64.a1', '64.c1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '64.264', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063420
    {'ambient': '256.29702', 'aut_centralizer_order': 32768, 'aut_label': '32.b1', 'aut_quo_index': 1249920, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.f1', '16.g1', '16.h1', '16.i1', '16.j1', '16.k1'], 'contains': ['64.a1', '64.b1', '64.d1'], 'core': '32.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5347, 5862, 5333, 5860], 'generators': [8, 160, 128], 'label': '256.29702.32.b1', 'mobius_quo': -8, 'mobius_sub': -1024, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.f1', '16.g1', '16.h1', '16.i1', '16.j1', '16.k1'], 'normal_contains': ['64.a1', '64.b1', '64.d1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '32.51', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063421
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '32.c1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.l1', '16.m1', '16.n1', '16.bf1', '16.bg1', '16.bh1', '16.bi1'], 'contains': ['64.b1', '64.c1', '64.s1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6871, 7897, 6852, 7892], 'generators': [2, 8, 128], 'label': '256.29702.32.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': ['16.a1', '16.l1', '16.m1', '16.n1'], 'normal_contains': ['64.b1', '64.c1'], 'normalizer': '1.a1', 'old_label': '32.c1', 'projective_image': '64.261', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063422
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.d1', 'aut_quo_index': 48, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['16.b1', '16.l1', '16.o1', '16.p1', '16.bj1', '16.bk1', '16.bl1', '16.bm1'], 'contains': ['64.b1', '64.e1', '64.t1'], 'core': '32.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [6787, 6838, 6768, 6835], 'generators': [6, 8, 128], 'label': '256.29702.32.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': ['16.b1', '16.l1', '16.o1', '16.p1'], 'normal_contains': ['64.b1'], 'normalizer': '1.a1', 'old_label': '32.d1', 'projective_image': '64.261', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063423
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '32.e1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.j1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.m1', '16.o1', '16.bn1', '16.bq1', '16.br1', '16.bs1'], 'contains': ['64.b1', '64.g1', '64.v1'], 'core': '32.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [7696, 6717, 7675, 6713], 'generators': [196, 8, 128], 'label': '256.29702.32.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': ['16.d1', '16.m1', '16.o1'], 'normal_contains': ['64.b1'], 'normalizer': '1.a1', 'old_label': '32.e1', 'projective_image': '64.261', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063424
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '16.a1', 'complements': ['128.i1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.e1', '4.f1', '4.h1', '4.q1', '4.r1', '4.bi1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4363, 8632, 4350, 8627], 'generators': [1, 2, 4, 160, 64], 'label': '256.29702.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.e1', '4.f1', '4.h1', '4.q1', '4.r1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063425
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.h1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 128, 'centralizer': '16.a1', 'complements': ['64.be1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.h1'], 'contains': ['8.b1', '8.e1', '8.g1', '8.s1', '8.bs1'], 'core': '4.h1', 'coset_action_label': None, 'count': 2, 'diagramx': [5037, 9192, 5021, 9189], 'generators': [1, 2, 64, 160], 'label': '256.29702.4.h1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1', 'normal_contained_in': ['2.a1', '2.h1'], 'normal_contains': ['8.b1', '8.e1', '8.g1', '8.s1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063426
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '32.f1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.l1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '16.m1', '16.p1', '16.bo1', '16.bt1', '16.bu1'], 'contains': ['64.b1', '64.h1', '64.w1'], 'core': '32.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [7397, 6960, 7376, 6956], 'generators': [198, 8, 128], 'label': '256.29702.32.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1', 'normal_contained_in': ['16.e1', '16.m1', '16.p1'], 'normal_contains': ['64.b1'], 'normalizer': '1.a1', 'old_label': '32.f1', 'projective_image': '64.261', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063427
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.g1', 'aut_quo_index': 48, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.o1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['16.g1', '16.n1', '16.o1', '16.p1', '16.bp1', '16.bv1', '16.bw1'], 'contains': ['64.b1', '64.j1'], 'core': '32.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [7584, 6555, 7563, 6551], 'generators': [64, 8], 'label': '256.29702.32.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1', 'normal_contained_in': ['16.g1', '16.n1', '16.o1', '16.p1'], 'normal_contains': ['64.b1'], 'normalizer': '1.a1', 'old_label': '32.g1', 'projective_image': '64.261', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063428
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.h1', 'aut_quo_index': 36, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['16.c1', '16.cc2', '16.cf2', '16.ci2', '16.cj2', '16.ck2', '16.cl2'], 'contains': ['64.d1', '64.n1', '64.u1'], 'core': '32.h1', 'coset_action_label': None, 'count': 8, 'diagramx': [1968, 4341, 1962, 4296], 'generators': [1, 8, 160], 'label': '256.29702.32.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.h1', 'normal_contained_in': ['16.c1'], 'normal_contains': ['64.d1'], 'normalizer': '1.a1', 'old_label': '32.h1', 'projective_image': '64.264', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063429
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '16.q1', '16.w1', '16.x1', '16.y1'], 'contains': ['64.a1', '64.e1', '64.m1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5517, -1, 5502, -1], 'generators': [6, 160, 128], 'label': '256.29702.32.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.i1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063430
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.i2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '16.q1', '16.w2', '16.x2', '16.y2'], 'contains': ['64.a1', '64.e1', '64.m2'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5602, -1, 5586, -1], 'generators': [6, 168, 128], 'label': '256.29702.32.i2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.i2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063431
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.c1', '16.r1', '16.w1', '16.w2', '16.z1', '16.ba1'], 'contains': ['64.a1', '64.f1', '64.n1', '64.n2'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2577, -1, 2570, -1], 'generators': [1, 160, 128], 'label': '256.29702.32.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.j1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063432
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.s1', '16.x1', '16.x2', '16.bb1', '16.bc1'], 'contains': ['64.a1', '64.g1', '64.o1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6956, -1, 6937, -1], 'generators': [196, 160, 128], 'label': '256.29702.32.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.k1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063433
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '16.s1', '16.y1', '16.y2', '16.bd1'], 'contains': ['64.a1', '64.h1', '64.p1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6702, -1, 6683, -1], 'generators': [198, 160, 128], 'label': '256.29702.32.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.l1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063434
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.f1', '16.t1', '16.z1', '16.bb1', '16.bd1'], 'contains': ['64.a1', '64.i1', '64.q1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5941, -1, 5924, -1], 'generators': [19, 160, 128], 'label': '256.29702.32.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '32.m1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063435
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.g1', '16.u1', '16.x1', '16.y2', '16.be1'], 'contains': ['64.a1', '64.j1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6428, -1, 6411, -1], 'generators': [64, 168], 'label': '256.29702.32.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '32.n1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063436
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.be1'], 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '2.g1', '2.h1'], 'contains': ['8.b1', '8.f1', '8.h1', '8.u1', '8.u2'], 'core': '4.i1', 'coset_action_label': None, 'count': 4, 'diagramx': [978, 6287, 974, 6285], 'generators': [1, 2, 80], 'label': '256.29702.4.i1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1', 'normal_contained_in': ['2.b1', '2.g1', '2.h1'], 'normal_contains': ['8.b1', '8.f1', '8.h1', '8.u1', '8.u2'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063437
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.n2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.g1', '16.u1', '16.x2', '16.y1', '16.be2'], 'contains': ['64.a1', '64.j1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6570, -1, 6551, -1], 'generators': [64, 160], 'label': '256.29702.32.n2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '32.n2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063438
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.be2', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.h1', '16.v1', '16.z1', '16.ba1', '16.be1', '16.be2'], 'contains': ['64.a1', '64.r1'], 'core': '64.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3854, -1, 3843, -1], 'generators': [80, 128], 'label': '256.29702.32.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1', 'old_label': '32.o1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063439
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.x1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.j1', '16.t1', '16.ba1', '16.bc1', '16.bd1'], 'contains': ['64.a1', '64.k1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7069, -1, 7049, -1], 'generators': [17, 160], 'label': '256.29702.32.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '32.p1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063443
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.j1', '16.bg1', '16.bm1', '16.br1', '16.bt1', '16.bw1'], 'contains': ['64.b1', '64.k1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9029, -1, 9004, -1], 'generators': [17, 8], 'label': '256.29702.32.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.t1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063444
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.k1', '16.bi1', '16.bk1', '16.bm1', '16.bs1', '16.bu1', '16.bv1', '16.bw1'], 'contains': ['64.b1', '64.z1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [8719, -1, 8694, -1], 'generators': [81, 128], 'label': '256.29702.32.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.u1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063445
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.l1', '16.q1', '16.bx1', '16.by1'], 'contains': ['64.c1', '64.e1', '64.ba1'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [5772, -1, 5755, -1], 'generators': [2, 4, 128], 'label': '256.29702.32.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.v1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063446
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.r1', '16.bf1', '16.bx1'], 'contains': ['64.c1', '64.f1', '64.bb1'], 'core': '64.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [3057, -1, 3048, -1], 'generators': [1, 2, 128], 'label': '256.29702.32.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.w1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063447
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.j1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 64, 'centralizer': '16.d1', 'complements': ['64.bd1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.f1'], 'contains': ['8.c1', '8.d1', '8.v1', '8.x1', '8.z1', '8.bm1', '8.bt1'], 'core': '4.j1', 'coset_action_label': None, 'count': 1, 'diagramx': [7950, 7835, 7928, 7833], 'generators': [17, 2, 196, 160, 8], 'label': '256.29702.4.j1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1', 'normal_contained_in': ['2.c1', '2.f1'], 'normal_contains': ['8.c1', '8.d1', '8.v1', '8.x1', '8.z1'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063448
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.m1', '16.s1', '16.by1', '16.bz1'], 'contains': ['64.c1', '64.g1', '64.h1', '64.bc1'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [7781, -1, 7759, -1], 'generators': [2, 196, 128], 'label': '256.29702.32.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.x1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063449
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.t1', '16.bg1', '16.bz1'], 'contains': ['64.c1', '64.i1', '64.k1'], 'core': '64.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [9136, -1, 9111, -1], 'generators': [17, 2], 'label': '256.29702.32.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '32.y1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063450
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.n1', '16.u1', '16.by1'], 'contains': ['64.c1', '64.j1'], 'core': '64.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [7209, -1, 7189, -1], 'generators': [2, 64], 'label': '256.29702.32.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '32.z1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063451
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.w1', '16.w2', '16.bj1', '16.bx1'], 'contains': ['64.e1', '64.f1', '64.bd1'], 'core': '128.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [2492, -1, 2485, -1], 'generators': [1, 6, 128], 'label': '256.29702.32.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.ba1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063452
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.o1', '16.x1', '16.x2', '16.by1'], 'contains': ['64.e1', '64.g1', '64.j1'], 'core': '128.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [7476, -1, 7455, -1], 'generators': [6, 196], 'label': '256.29702.32.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.bb1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063453
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.p1', '16.y1', '16.y2', '16.by1'], 'contains': ['64.e1', '64.h1', '64.j1'], 'core': '128.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [7317, -1, 7297, -1], 'generators': [6, 64], 'label': '256.29702.32.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.bc1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063454
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.bb1', '16.bq1', '16.bz1'], 'contains': ['64.g1', '64.i1', '64.be1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8916, -1, 8891, -1], 'generators': [19, 196, 128], 'label': '256.29702.32.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '32.bd1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063455
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.x1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.bc1', '16.br1', '16.bz1'], 'contains': ['64.g1', '64.k1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [9318, -1, 9292, -1], 'generators': [17, 196], 'label': '256.29702.32.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '32.be1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063456
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.bd1', '16.bt1', '16.bz1'], 'contains': ['64.h1', '64.i1', '64.k1'], 'core': '128.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [9211, -1, 9185, -1], 'generators': [17, 198], 'label': '256.29702.32.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.z1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '32.bf1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063457
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.q1', '16.ca1', '16.cb1'], 'contains': ['64.l1', '64.m1', '64.m2', '64.ba1'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [1628, -1, 1624, -1], 'generators': [2, 4, 32], 'label': '256.29702.32.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bg1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063458
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '2688.ei', 'aut_weyl_index': 128, 'centralizer': '32.b1', 'complements': ['64.bd1'], 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '2.f1', '2.g1'], 'contains': ['8.c1', '8.f1', '8.w1', '8.ba1'], 'core': '4.k1', 'coset_action_label': None, 'count': 2, 'diagramx': [4060, 7228, 4047, 7225], 'generators': [2, 20, 80], 'label': '256.29702.4.k1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1', 'normal_contained_in': ['2.d1', '2.f1', '2.g1'], 'normal_contains': ['8.c1', '8.f1', '8.w1', '8.ba1'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063459
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.r1', '16.ca1', '16.cc1', '16.cc2'], 'contains': ['64.l1', '64.n1', '64.n2', '64.bb1'], 'core': '128.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [1543, -1, 1539, -1], 'generators': [1, 2, 32], 'label': '256.29702.32.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bh1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063460
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.s1', '16.cd1'], 'contains': ['64.l1', '64.o1', '64.p1', '64.bc1'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [5432, -1, 5417, -1], 'generators': [2, 196, 32], 'label': '256.29702.32.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '32.bi1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063461
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.w1', '16.ca1', '16.cf1'], 'contains': ['64.m1', '64.n2', '64.bd1'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [921, -1, 919, -1], 'generators': [1, 6, 32], 'label': '256.29702.32.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bj1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063462
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '32.bj2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.w1', '16.ca1', '16.cf2'], 'contains': ['64.m1', '64.n1', '64.bd1'], 'core': '128.b1', 'coset_action_label': None, 'count': 64, 'diagramx': [1138, -1, 1135, -1], 'generators': [1, 6, 160], 'label': '256.29702.32.bj2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bj2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063463
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '32.bj3', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.w2', '16.ca1', '16.cf1', '16.cf2'], 'contains': ['64.m2', '64.n1', '64.n2', '64.bd1'], 'core': '128.b1', 'coset_action_label': None, 'count': 128, 'diagramx': [1289, -1, 1285, -1], 'generators': [1, 6, 40], 'label': '256.29702.32.bj3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bj3', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063466
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '16.cb1', '16.cc1', '16.cc2', '16.cd1', '16.ce1'], 'contains': ['64.d1', '64.l1', '64.s1'], 'core': '64.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [2887, -1, 2879, -1], 'generators': [2, 136, 160], 'label': '256.29702.32.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.bm1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063467
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.b1', '16.cb1', '16.cf1', '16.cf2', '16.cg1', '16.ch1'], 'contains': ['64.d1', '64.m1', '64.m2', '64.t1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [1798, -1, 1793, -1], 'generators': [6, 136, 160], 'label': '256.29702.32.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.bn1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063468
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.c1', '16.cc1', '16.cf1', '16.cf2', '16.ck1', '16.cl1'], 'contains': ['64.d1', '64.n1', '64.n2', '64.u2'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [1459, -1, 1455, -1], 'generators': [1, 136, 160], 'label': '256.29702.32.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.bo1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063469
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.l1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 64, 'centralizer': '16.e1', 'complements': ['64.bd1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.g1'], 'contains': ['8.c1', '8.h1', '8.y1', '8.bb1', '8.bu1'], 'core': '4.l1', 'coset_action_label': None, 'count': 1, 'diagramx': [6775, 8512, 6755, 8509], 'generators': [21, 2, 196, 160], 'label': '256.29702.4.l1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1', 'normal_contained_in': ['2.c1', '2.g1'], 'normal_contains': ['8.c1', '8.h1', '8.y1', '8.bb1'], 'normalizer': '1.a1', 'old_label': '4.l1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.l1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063470
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bo2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '16.cc2', '16.cf1', '16.ci1', '16.cj1'], 'contains': ['64.d1', '64.n2', '64.u1'], 'core': '64.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [2407, -1, 2401, -1], 'generators': [1, 8, 32], 'label': '256.29702.32.bo2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.bo2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063471
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '16.cd1', '16.ci1', '16.ci2', '16.cm1', '16.cn1'], 'contains': ['64.d1', '64.o1', '64.v1'], 'core': '64.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [3741, -1, 3731, -1], 'generators': [196, 136, 160], 'label': '256.29702.32.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '32.bp1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063472
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.e1', '16.cd1', '16.cj1', '16.cj2', '16.co1', '16.cp1'], 'contains': ['64.d1', '64.p1', '64.w1'], 'core': '64.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [3582, -1, 3572, -1], 'generators': [198, 136, 160], 'label': '256.29702.32.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '32.bq1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063473
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.f1', '16.cg1', '16.ck1', '16.ck2', '16.cm1', '16.cq1'], 'contains': ['64.d1', '64.q1', '64.x1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [3141, -1, 3133, -1], 'generators': [19, 136, 160], 'label': '256.29702.32.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1', 'old_label': '32.br1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063474
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.be2', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.h1', '16.ch1', '16.ck1', '16.cl2', '16.co1', '16.cr1'], 'contains': ['64.d1', '64.r1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [2154, -1, 2148, -1], 'generators': [80, 8], 'label': '256.29702.32.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1', 'old_label': '32.bs1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063475
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bs2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.be2', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.h1', '16.ch1', '16.ck2', '16.cl1', '16.cn1', '16.cq1'], 'contains': ['64.d1', '64.r1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [2294, -1, 2289, -1], 'generators': [80, 136], 'label': '256.29702.32.bs2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1', 'old_label': '32.bs2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063476
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bt1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.i1', '16.ce1', '16.ci1', '16.cj2', '16.cr1'], 'contains': ['64.d1', '64.y1'], 'core': '64.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [3254, -1, 3245, -1], 'generators': [65, 160], 'label': '256.29702.32.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '32.bt1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063477
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bt2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.i1', '16.ce1', '16.ci2', '16.cj1', '16.cq1'], 'contains': ['64.d1', '64.y1'], 'core': '64.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [3395, -1, 3385, -1], 'generators': [65, 32], 'label': '256.29702.32.bt2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '32.bt2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063478
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.k1', '16.cg1', '16.cl1', '16.cl2', '16.cp1', '16.cr1'], 'contains': ['64.d1', '64.z1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [2775, -1, 2767, -1], 'generators': [81, 32], 'label': '256.29702.32.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1', 'old_label': '32.bu1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063479
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.l1', '16.cb1', '16.cs1'], 'contains': ['64.s1', '64.t1', '64.ba1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [2972, -1, 2964, -1], 'generators': [2, 4, 136], 'label': '256.29702.32.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bv1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063480
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.m1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 128, 'centralizer': '32.b1', 'complements': ['64.bd1'], 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '2.h1'], 'contains': ['8.d1', '8.e1', '8.h1', '8.bc1', '8.bf1', '8.bv1'], 'core': '4.m1', 'coset_action_label': None, 'count': 2, 'diagramx': [7280, 7514, 7260, 7512], 'generators': [17, 2, 64, 160], 'label': '256.29702.4.m1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1', 'normal_contained_in': ['2.c1', '2.h1'], 'normal_contains': ['8.d1', '8.e1', '8.h1', '8.bc1', '8.bf1'], 'normalizer': '1.a1', 'old_label': '4.m1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.m1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063481
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.bw1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.bf1', '16.cc1', '16.cs1'], 'contains': ['64.s1', '64.u2', '64.bb1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [1882, -1, 1877, -1], 'generators': [1, 2, 136], 'label': '256.29702.32.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bw1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063482
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.bw2', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.bf1', '16.cc2', '16.cs1', '16.ct1'], 'contains': ['64.s1', '64.u1', '64.bb1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [2662, -1, 2654, -1], 'generators': [1, 2, 8], 'label': '256.29702.32.bw2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.bw2', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bw2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063483
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '8.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.m1', '16.cd1', '16.ct1'], 'contains': ['64.s1', '64.v1', '64.w1', '64.bc1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [4407, -1, 4395, -1], 'generators': [2, 196, 136], 'label': '256.29702.32.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '32.bx1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063484
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.by1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.g1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.bh1', '16.ce1', '16.ct1'], 'contains': ['64.s1', '64.y1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [4079, -1, 4068, -1], 'generators': [65, 2], 'label': '256.29702.32.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '32.by1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.by1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063485
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '32.bz1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['16.bj1', '16.cf1', '16.cf2', '16.cs1'], 'contains': ['64.t1', '64.u1', '64.u2', '64.bd1'], 'core': '128.c1', 'coset_action_label': None, 'count': 128, 'diagramx': [1713, -1, 1708, -1], 'generators': [1, 6, 136], 'label': '256.29702.32.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.bz1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063486
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.ca1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.bk1', '16.cg1'], 'contains': ['64.t1', '64.x1', '64.z1'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [4187, -1, 4175, -1], 'generators': [81, 6], 'label': '256.29702.32.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.l1', 'old_label': '32.ca1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ca1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063487
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.cb1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.bn1', '16.ci1', '16.ci2', '16.ct1'], 'contains': ['64.u1', '64.v1', '64.y1'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [3662, -1, 3651, -1], 'generators': [1, 196], 'label': '256.29702.32.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '32.cb1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063488
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 65536, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.bo1', '16.cj1', '16.cj2', '16.ct1'], 'contains': ['64.u1', '64.w1', '64.y1'], 'core': '128.c1', 'coset_action_label': None, 'count': 64, 'diagramx': [3503, -1, 3493, -1], 'generators': [1, 198], 'label': '256.29702.32.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '32.cc1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063489
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.cd1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.bq1', '16.cm1'], 'contains': ['64.v1', '64.x1', '64.be1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [6025, -1, 6009, -1], 'generators': [19, 196, 136], 'label': '256.29702.32.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.v1', 'old_label': '32.cd1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063490
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '32.ce1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.bu1', '16.cp1'], 'contains': ['64.w1', '64.z1'], 'core': '128.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [4294, -1, 4282, -1], 'generators': [21, 198], 'label': '256.29702.32.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bb1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1', 'old_label': '32.ce1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ce1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063491
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.n1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.bd1'], 'conjugacy_class_count': 4, 'contained_in': ['2.e1', '2.f1', '2.h1'], 'contains': ['8.d1', '8.f1', '8.g1', '8.bd1', '8.bg1'], 'core': '4.n1', 'coset_action_label': None, 'count': 4, 'diagramx': [4177, 6455, 4164, 6453], 'generators': [17, 2, 80], 'label': '256.29702.4.n1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1', 'normal_contained_in': ['2.e1', '2.f1', '2.h1'], 'normal_contains': ['8.d1', '8.f1', '8.g1', '8.bd1', '8.bg1'], 'normalizer': '1.a1', 'old_label': '4.n1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.n1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063492
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '32.cf1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '8.3', 'aut_weyl_index': 32768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['16.bx1', '16.ca1', '16.cs1'], 'contains': ['64.ba1', '64.bb1', '64.bd1'], 'core': '256.a1', 'coset_action_label': '32T3438', 'count': 512, 'diagramx': [1374, -1, 1370, -1], 'generators': [1, 2, 4], 'label': '256.29702.32.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.cf1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063493
    {'ambient': '256.29702', 'aut_centralizer_order': 65536, 'aut_label': '64.a1', 'aut_quo_index': 288, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '32.b1', '32.i1', '32.i2', '32.j1', '32.k1', '32.l1', '32.m1', '32.n1', '32.n2', '32.o1', '32.p1'], 'contains': ['128.a1', '128.b1'], 'core': '64.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5772, 6549, 5755, 6545], 'generators': [160, 128], 'label': '256.29702.64.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1'], 'normal_contains': ['128.a1', '128.b1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '64.264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.264', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063494
    {'ambient': '256.29702', 'aut_centralizer_order': 131072, 'aut_label': '64.b1', 'aut_quo_index': 2688, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1', '32.c1', '32.d1', '32.e1', '32.f1', '32.g1', '32.q1', '32.r1', '32.s1', '32.t1', '32.u1'], 'contains': ['128.a1', '128.c1'], 'core': '64.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7260, 6717, 7240, 6713], 'generators': [8, 128], 'label': '256.29702.64.b1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': ['32.b1', '32.c1', '32.d1', '32.e1', '32.f1', '32.g1'], 'normal_contains': ['128.a1', '128.c1'], 'normalizer': '1.a1', 'old_label': '64.b1', 'projective_image': '64.261', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.261', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063495
    {'ambient': '256.29702', 'aut_centralizer_order': 32768, 'aut_label': '64.c1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['32.a1', '32.c1', '32.v1', '32.w1', '32.x1', '32.y1', '32.z1'], 'contains': ['128.a1', '128.d1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [6871, 7423, 6852, 7337], 'generators': [2, 128], 'label': '256.29702.64.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1', 'normal_contained_in': ['32.a1', '32.c1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.c1', 'projective_image': '128.2177', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.46', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063496
    {'ambient': '256.29702', 'aut_centralizer_order': 32768, 'aut_label': '64.d1', 'aut_quo_index': 576, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['32.b1', '32.h1', '32.bm1', '32.bn1', '32.bo1', '32.bo2', '32.bp1', '32.bq1', '32.br1', '32.bs1', '32.bs2', '32.bt1', '32.bt2', '32.bu1'], 'contains': ['128.b1', '128.c1'], 'core': '64.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [2718, 6122, 2710, 6170], 'generators': [136, 160], 'label': '256.29702.64.d1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.d1', 'normal_contained_in': ['32.b1', '32.h1'], 'normal_contains': ['128.b1', '128.c1'], 'normalizer': '1.a1', 'old_label': '64.d1', 'projective_image': '64.264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.264', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063497
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.d1', '32.i1', '32.i2', '32.v1', '32.ba1', '32.bb1', '32.bc1'], 'contains': ['128.a1', '128.e1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5856, -1, 5840, -1], 'generators': [6, 128], 'label': '256.29702.64.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.e1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063498
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.j1', '32.q1', '32.w1', '32.ba1'], 'contains': ['128.a1', '128.f1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3057, -1, 3048, -1], 'generators': [1, 128], 'label': '256.29702.64.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.f1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063499
    {'ambient': '256.29702', 'aut_centralizer_order': 32768, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.e1', '32.k1', '32.x1', '32.bb1', '32.bd1', '32.be1'], 'contains': ['128.a1', '128.g1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7587, -1, 7565, -1], 'generators': [196, 128], 'label': '256.29702.64.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '64.g1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063500
    {'ambient': '256.29702', 'aut_centralizer_order': 32768, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.f1', '32.l1', '32.x1', '32.bc1', '32.bf1'], 'contains': ['128.a1', '128.h1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7345, -1, 7324, -1], 'generators': [198, 128], 'label': '256.29702.64.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '64.h1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063501
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.m1', '32.r1', '32.y1', '32.bd1', '32.bf1'], 'contains': ['128.a1', '128.i1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8831, -1, 8807, -1], 'generators': [19, 128], 'label': '256.29702.64.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '64.i1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063502
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.o1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2688.ei', 'aut_weyl_index': 128, 'centralizer': '16.g1', 'complements': ['64.bd1', '64.be1'], 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '2.h1'], 'contains': ['8.e1', '8.f1', '8.be1', '8.be2', '8.bn1'], 'core': '4.o1', 'coset_action_label': None, 'count': 2, 'diagramx': [5275, 6956, 5259, 6953], 'generators': [2, 20, 64, 160], 'label': '256.29702.4.o1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1', 'normal_contained_in': ['2.d1', '2.h1'], 'normal_contains': ['8.e1', '8.f1', '8.be1', '8.be2'], 'normalizer': '1.a1', 'old_label': '4.o1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.o1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063503
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.g1', '32.n1', '32.n2', '32.z1', '32.bb1', '32.bc1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7181, -1, 7160, -1], 'generators': [64], 'label': '256.29702.64.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '64.j1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063504
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '8.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.p1', '32.t1', '32.y1', '32.be1', '32.bf1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9082, -1, 9057, -1], 'generators': [17], 'label': '256.29702.64.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '64.k1', 'projective_image': '128.2177', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063505
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.a1', '32.bg1', '32.bh1', '32.bi1', '32.bm1'], 'contains': ['128.b1', '128.d1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [2887, -1, 2879, -1], 'generators': [2, 32], 'label': '256.29702.64.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.l1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063508
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.h1', '32.j1', '32.bh1', '32.bj2', '32.bj3', '32.bk1', '32.bo1'], 'contains': ['128.b1', '128.f1'], 'core': '128.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [1925, -1, 1919, -1], 'generators': [1, 160], 'label': '256.29702.64.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.n1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063509
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '64.n2', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.j1', '32.bh1', '32.bj1', '32.bj3', '32.bo1', '32.bo2'], 'contains': ['128.b1', '128.f1'], 'core': '128.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [1628, -1, 1624, -1], 'generators': [1, 32], 'label': '256.29702.64.n2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.n2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063510
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.k1', '32.bi1', '32.bl1', '32.bp1'], 'contains': ['128.b1', '128.g1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4507, -1, 4494, -1], 'generators': [196, 32], 'label': '256.29702.64.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '64.o1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063511
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.l1', '32.bi1', '32.bq1'], 'contains': ['128.b1', '128.h1'], 'core': '128.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [4337, -1, 4325, -1], 'generators': [198, 32], 'label': '256.29702.64.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '64.p1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063512
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.m1', '32.bk1', '32.bl1', '32.br1'], 'contains': ['128.b1', '128.i1'], 'core': '128.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [3830, -1, 3827, -1], 'generators': [19, 32], 'label': '256.29702.64.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1', 'old_label': '64.q1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063513
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.p1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.be1', '64.bd1'], 'conjugacy_class_count': 4, 'contained_in': ['2.e1', '2.g1', '2.h1'], 'contains': ['8.f1', '8.g1', '8.h1', '8.bh1', '8.bh2'], 'core': '4.p1', 'coset_action_label': None, 'count': 4, 'diagramx': [3664, 6653, 3652, 6652], 'generators': [21, 2, 80], 'label': '256.29702.4.p1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1', 'normal_contained_in': ['2.e1', '2.g1', '2.h1'], 'normal_contains': ['8.f1', '8.g1', '8.h1', '8.bh1', '8.bh2'], 'normalizer': '1.a1', 'old_label': '4.p1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.p1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063514
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '8.be2', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.o1', '32.bk1', '32.bs1', '32.bs2'], 'contains': ['128.b1'], 'core': '128.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [2343, -1, 2337, -1], 'generators': [80], 'label': '256.29702.64.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bg2', 'old_label': '64.r1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063515
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.c1', '32.bm1', '32.bv1', '32.bw1', '32.bw2', '32.bx1', '32.by1'], 'contains': ['128.c1', '128.d1'], 'core': '128.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [3282, -1, 3313, -1], 'generators': [2, 136], 'label': '256.29702.64.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.s1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063516
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.d1', '32.bn1', '32.bv1', '32.bz1', '32.ca1'], 'contains': ['128.c1', '128.e1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [2972, -1, 2964, -1], 'generators': [6, 136], 'label': '256.29702.64.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '64.t1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063517
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.u1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.h1', '32.q1', '32.bo2', '32.bw2', '32.bz1', '32.cb1', '32.cc1'], 'contains': ['128.c1', '128.f1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [2802, -1, 2795, -1], 'generators': [1, 8], 'label': '256.29702.64.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.u1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063518
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.u2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.q1', '32.bo1', '32.bw1', '32.bz1'], 'contains': ['128.c1', '128.f1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [2264, -1, 2258, -1], 'generators': [1, 136], 'label': '256.29702.64.u2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.u2', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.u2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063519
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.e1', '32.bp1', '32.bx1', '32.cb1', '32.cd1'], 'contains': ['128.c1', '128.g1'], 'core': '128.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [4421, -1, 4409, -1], 'generators': [196, 136], 'label': '256.29702.64.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '64.v1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063520
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.f1', '32.bq1', '32.bx1', '32.cc1', '32.ce1'], 'contains': ['128.c1', '128.h1'], 'core': '128.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [4252, -1, 4240, -1], 'generators': [198, 136], 'label': '256.29702.64.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '64.w1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063521
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.r1', '32.br1', '32.ca1', '32.cd1'], 'contains': ['128.c1', '128.i1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [4591, -1, 4578, -1], 'generators': [19, 136], 'label': '256.29702.64.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '64.x1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063522
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.y1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '8.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.s1', '32.bt1', '32.bt2', '32.by1', '32.cb1', '32.cc1'], 'contains': ['128.c1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [3582, -1, 3572, -1], 'generators': [65], 'label': '256.29702.64.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '64.y1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063523
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.u1', '32.bu1', '32.ca1', '32.ce1'], 'contains': ['128.c1'], 'core': '128.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [4173, -1, 4161, -1], 'generators': [81], 'label': '256.29702.64.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1', 'old_label': '64.z1', 'projective_image': '128.2216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063524
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.q1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.i1', '2.j1'], 'contains': ['8.i1', '8.j1', '8.n1', '8.p1', '8.s1', '8.bw1'], 'core': '4.q1', 'coset_action_label': None, 'count': 4, 'diagramx': [4363, 4221, 4350, 4220], 'generators': [1, 6, 196, 160], 'label': '256.29702.4.q1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.q1', 'normal_contained_in': ['2.a1', '2.i1', '2.j1'], 'normal_contains': ['8.i1', '8.j1', '8.n1', '8.p1', '8.s1'], 'normalizer': '1.a1', 'old_label': '4.q1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063525
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.v1', '32.bg1', '32.bv1', '32.cf1'], 'contains': ['128.d1', '128.e1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [2179, -1, 2173, -1], 'generators': [2, 4], 'label': '256.29702.64.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.ba1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063526
    {'ambient': '256.29702', 'aut_centralizer_order': 1024, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['32.w1', '32.bh1', '32.bw1', '32.bw2', '32.cf1'], 'contains': ['128.d1', '128.f1'], 'core': '256.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [2094, -1, 2089, -1], 'generators': [1, 2], 'label': '256.29702.64.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.bb1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063527
    {'ambient': '256.29702', 'aut_centralizer_order': 4096, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '8.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.x1', '32.bi1', '32.bx1'], 'contains': ['128.d1', '128.g1', '128.h1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [4675, -1, 4663, -1], 'generators': [2, 196], 'label': '256.29702.64.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '64.bc1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063528
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': 256, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 64, 'contained_in': ['32.ba1', '32.bj1', '32.bj2', '32.bj3', '32.bz1', '32.cf1'], 'contains': ['128.e1', '128.f1'], 'core': '256.a1', 'coset_action_label': None, 'count': 256, 'diagramx': [1502, -1, 1497, -1], 'generators': [1, 6], 'label': '256.29702.64.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.bd1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063529
    {'ambient': '256.29702', 'aut_centralizer_order': 2048, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 131072, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.bd1', '32.bl1', '32.cd1'], 'contains': ['128.g1', '128.i1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [5941, -1, 5924, -1], 'generators': [19, 196], 'label': '256.29702.64.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.v1', 'old_label': '64.be1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063530
    {'ambient': '256.29702', 'aut_centralizer_order': 262144, 'aut_label': '128.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.c1', '64.e1', '64.f1', '64.g1', '64.h1', '64.i1', '64.j1', '64.k1'], 'contains': ['256.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7181, 6717, 7160, 6713], 'generators': [128], 'label': '256.29702.128.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1', 'normal_contained_in': ['64.a1', '64.b1', '64.c1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.a1', 'projective_image': '128.2177', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2177', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063531
    {'ambient': '256.29702', 'aut_centralizer_order': 65536, 'aut_label': '128.b1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['64.a1', '64.d1', '64.l1', '64.m1', '64.m2', '64.n1', '64.n2', '64.o1', '64.p1', '64.q1', '64.r1'], 'contains': ['256.a1'], 'core': '128.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2802, 6503, 2795, 6499], 'generators': [32], 'label': '256.29702.128.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1', 'normal_contained_in': ['64.a1', '64.d1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.b1', 'projective_image': '128.2264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2264', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063532
    {'ambient': '256.29702', 'aut_centralizer_order': 131072, 'aut_label': '128.c1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['64.b1', '64.d1', '64.s1', '64.t1', '64.u1', '64.u2', '64.v1', '64.w1', '64.x1', '64.y1', '64.z1'], 'contains': ['256.a1'], 'core': '128.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [3582, 6610, 3572, 6606], 'generators': [136], 'label': '256.29702.128.c1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.c1', 'normal_contained_in': ['64.b1', '64.d1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.c1', 'projective_image': '128.2216', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2216', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063533
    {'ambient': '256.29702', 'aut_centralizer_order': 32768, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.c1', '64.l1', '64.s1', '64.ba1', '64.bb1', '64.bc1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3282, -1, 3313, -1], 'generators': [2], 'label': '256.29702.128.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '128.d1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063534
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.e1', '64.m1', '64.m2', '64.t1', '64.ba1', '64.bd1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2179, -1, 2173, -1], 'generators': [6], 'label': '256.29702.128.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '128.e1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063535
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 16, 'centralizer': '32.b1', 'complements': ['128.g1', '128.h1', '128.i1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.d1', '4.g1', '4.i1', '4.s1', '4.t1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1212, 6587, 1208, 6584], 'generators': [1, 2, 4, 80], 'label': '256.29702.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.d1', '4.g1', '4.i1', '4.s1', '4.t1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063536
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.r1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '16.a1', 'complements': ['64.be1'], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.k1'], 'contains': ['8.i1', '8.k1', '8.n1', '8.q1', '8.s1', '8.bx1'], 'core': '4.r1', 'coset_action_label': None, 'count': 4, 'diagramx': [3872, 4592, 3861, 4590], 'generators': [1, 6, 64, 160], 'label': '256.29702.4.r1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.r1', 'normal_contained_in': ['2.a1', '2.k1'], 'normal_contains': ['8.i1', '8.k1', '8.n1', '8.q1', '8.s1'], 'normalizer': '1.a1', 'old_label': '4.r1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.r1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063537
    {'ambient': '256.29702', 'aut_centralizer_order': 8192, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['64.f1', '64.n1', '64.n2', '64.u1', '64.u2', '64.bb1', '64.bd1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2099, -1, 2094, -1], 'generators': [1], 'label': '256.29702.128.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '128.f1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063538
    {'ambient': '256.29702', 'aut_centralizer_order': 32768, 'aut_label': '128.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '4.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.g1', '64.o1', '64.v1', '64.bc1', '64.be1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4512, -1, 4499, -1], 'generators': [196], 'label': '256.29702.128.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '128.g1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063539
    {'ambient': '256.29702', 'aut_centralizer_order': 32768, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '4.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.h1', '64.p1', '64.w1', '64.bc1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4337, -1, 4325, -1], 'generators': [198], 'label': '256.29702.128.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '128.h1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063540
    {'ambient': '256.29702', 'aut_centralizer_order': 16384, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 262144, 'centralizer': '8.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.i1', '64.q1', '64.x1', '64.be1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4591, -1, 4578, -1], 'generators': [19], 'label': '256.29702.128.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.v1', 'old_label': '128.i1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063541
    {'ambient': '256.29702', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1', '128.b1', '128.c1', '128.d1', '128.e1', '128.f1', '128.g1', '128.h1', '128.i1'], 'contains': [], 'core': '256.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3582, 6610, 3572, 6606], 'generators': [], 'label': '256.29702.256.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1', 'normal_contained_in': ['128.a1', '128.b1', '128.c1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '256.a1', 'projective_image': '256.29702', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063542
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.s1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.bc1'], 'conjugacy_class_count': 8, 'contained_in': ['2.b1', '2.i1', '2.k1'], 'contains': ['8.i1', '8.l1', '8.m1', '8.r1', '8.u1', '8.u2', '8.cd1'], 'core': '4.s1', 'coset_action_label': None, 'count': 8, 'diagramx': [674, 1941, 671, 1940], 'generators': [1, 6, 80, 128], 'label': '256.29702.4.s1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.s1', 'normal_contained_in': ['2.b1', '2.i1', '2.k1'], 'normal_contains': ['8.i1', '8.l1', '8.m1', '8.r1', '8.u1', '8.u2'], 'normalizer': '1.a1', 'old_label': '4.s1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.s1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063543
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.t1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.bc1', '64.be1'], 'conjugacy_class_count': 8, 'contained_in': ['2.b1', '2.j1', '2.k1'], 'contains': ['8.i1', '8.m1', '8.o1', '8.t1', '8.u1', '8.u2'], 'core': '4.t1', 'coset_action_label': None, 'count': 8, 'diagramx': [861, 499, 858, 499], 'generators': [5, 6, 80], 'label': '256.29702.4.t1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.t1', 'normal_contained_in': ['2.b1', '2.j1', '2.k1'], 'normal_contains': ['8.i1', '8.m1', '8.o1', '8.t1', '8.u1', '8.u2'], 'normalizer': '1.a1', 'old_label': '4.t1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.t1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063544
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.u1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 128, 'centralizer': '32.b1', 'complements': ['64.bd1', '64.bb1'], 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '2.i1'], 'contains': ['8.j1', '8.l1', '8.v1', '8.y1', '8.bc1', '8.by1'], 'core': '4.u1', 'coset_action_label': None, 'count': 2, 'diagramx': [7011, 5648, 6991, 5646], 'generators': [21, 6, 196, 160], 'label': '256.29702.4.u1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1', 'normal_contained_in': ['2.c1', '2.i1'], 'normal_contains': ['8.j1', '8.l1', '8.v1', '8.y1', '8.bc1'], 'normalizer': '1.a1', 'old_label': '4.u1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.u1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063545
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.v1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.bb1', '64.bd1'], 'conjugacy_class_count': 4, 'contained_in': ['2.d1', '2.i1', '2.j1'], 'contains': ['8.j1', '8.m1', '8.w1', '8.be1', '8.be2'], 'core': '4.v1', 'coset_action_label': None, 'count': 4, 'diagramx': [4849, 3693, 4834, 3691], 'generators': [18, 4, 64], 'label': '256.29702.4.v1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.v1', 'normal_contained_in': ['2.d1', '2.i1', '2.j1'], 'normal_contains': ['8.j1', '8.m1', '8.w1', '8.be1', '8.be2'], 'normalizer': '1.a1', 'old_label': '4.v1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.v1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063546
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.w1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 128, 'centralizer': '32.b1', 'complements': ['64.bd1', '64.bb1'], 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '2.j1'], 'contains': ['8.j1', '8.o1', '8.x1', '8.y1', '8.bf1', '8.bz1'], 'core': '4.w1', 'coset_action_label': None, 'count': 2, 'diagramx': [7727, 4980, 7706, 4978], 'generators': [17, 6, 196, 160], 'label': '256.29702.4.w1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1', 'normal_contained_in': ['2.c1', '2.j1'], 'normal_contains': ['8.j1', '8.o1', '8.x1', '8.y1', '8.bf1'], 'normalizer': '1.a1', 'old_label': '4.w1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.w1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063547
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.x1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.bd1', '64.bb1'], 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '2.k1'], 'contains': ['8.k1', '8.l1', '8.o1', '8.z1', '8.bb1', '8.bc1', '8.bf1', '8.ca1'], 'core': '4.x1', 'coset_action_label': None, 'count': 4, 'diagramx': [6569, 5323, 6550, 5321], 'generators': [17, 6, 64, 160], 'label': '256.29702.4.x1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.x1', 'normal_contained_in': ['2.c1', '2.k1'], 'normal_contains': ['8.k1', '8.l1', '8.o1', '8.z1', '8.bb1', '8.bc1', '8.bf1'], 'normalizer': '1.a1', 'old_label': '4.x1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.x1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063548
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.y1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.be1', '64.bb1', '64.bd1'], 'conjugacy_class_count': 4, 'contained_in': ['2.d1', '2.k1'], 'contains': ['8.k1', '8.m1', '8.ba1', '8.be1', '8.be2'], 'core': '4.y1', 'coset_action_label': None, 'count': 4, 'diagramx': [4689, 3921, 4675, 3920], 'generators': [18, 4, 80], 'label': '256.29702.4.y1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.y1', 'normal_contained_in': ['2.d1', '2.k1'], 'normal_contains': ['8.k1', '8.m1', '8.ba1', '8.be1', '8.be2'], 'normalizer': '1.a1', 'old_label': '4.y1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.y1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063549
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.z1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.bc1', '64.bd1', '64.bb1'], 'conjugacy_class_count': 8, 'contained_in': ['2.e1', '2.i1', '2.k1'], 'contains': ['8.l1', '8.m1', '8.n1', '8.bd1', '8.bh1', '8.bh2'], 'core': '4.z1', 'coset_action_label': None, 'count': 8, 'diagramx': [2912, 3429, 2903, 3428], 'generators': [21, 6, 80], 'label': '256.29702.4.z1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.z1', 'normal_contained_in': ['2.e1', '2.i1', '2.k1'], 'normal_contains': ['8.l1', '8.m1', '8.n1', '8.bd1', '8.bh1', '8.bh2'], 'normalizer': '1.a1', 'old_label': '4.z1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.z1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063550
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.ba1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.bc1', '64.be1', '64.bd1', '64.bb1'], 'conjugacy_class_count': 8, 'contained_in': ['2.e1', '2.j1', '2.k1'], 'contains': ['8.m1', '8.n1', '8.o1', '8.bg1', '8.bh1', '8.bh2'], 'core': '4.ba1', 'coset_action_label': None, 'count': 8, 'diagramx': [3228, 2232, 3218, 2231], 'generators': [17, 6, 80], 'label': '256.29702.4.ba1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ba1', 'normal_contained_in': ['2.e1', '2.j1', '2.k1'], 'normal_contains': ['8.m1', '8.n1', '8.o1', '8.bg1', '8.bh1', '8.bh2'], 'normalizer': '1.a1', 'old_label': '4.ba1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ba1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063551
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.djl', 'aut_weyl_index': 8, 'centralizer': '32.b1', 'complements': ['128.f1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.j1', '4.l1', '4.m1', '4.u1', '4.w1', '4.x1', '4.bj1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7145, 7514, 7125, 7512], 'generators': [17, 2, 4, 160, 64], 'label': '256.29702.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.j1', '4.l1', '4.m1', '4.u1', '4.w1', '4.x1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063552
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.bb1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.ba1', '64.bd1', '64.bb1'], 'conjugacy_class_count': 4, 'contained_in': ['2.f1', '2.i1'], 'contains': ['8.p1', '8.r1', '8.v1', '8.w1', '8.bd1', '8.ce1'], 'core': '4.bb1', 'coset_action_label': None, 'count': 4, 'diagramx': [2520, 2523, 2512, 2522], 'generators': [1, 18, 196, 128], 'label': '256.29702.4.bb1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bb1', 'normal_contained_in': ['2.f1', '2.i1'], 'normal_contains': ['8.p1', '8.r1', '8.v1', '8.w1', '8.bd1'], 'normalizer': '1.a1', 'old_label': '4.bb1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bb1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063553
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.bc1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.bd1', '64.ba1', '64.bb1'], 'conjugacy_class_count': 4, 'contained_in': ['2.f1', '2.j1'], 'contains': ['8.p1', '8.t1', '8.w1', '8.x1', '8.bg1'], 'core': '4.bc1', 'coset_action_label': None, 'count': 4, 'diagramx': [3525, 1193, 3514, 1193], 'generators': [17, 18, 196], 'label': '256.29702.4.bc1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bc1', 'normal_contained_in': ['2.f1', '2.j1'], 'normal_contains': ['8.p1', '8.t1', '8.w1', '8.x1', '8.bg1'], 'normalizer': '1.a1', 'old_label': '4.bc1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bc1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063554
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.bd1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.ba1', '64.bd1', '64.bb1'], 'conjugacy_class_count': 8, 'contained_in': ['2.g1', '2.i1', '2.j1'], 'contains': ['8.p1', '8.u1', '8.u2', '8.w1', '8.y1', '8.bh1', '8.bh2'], 'core': '4.bd1', 'coset_action_label': None, 'count': 8, 'diagramx': [1923, 1608, 1916, 1607], 'generators': [5, 18, 196], 'label': '256.29702.4.bd1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bd1', 'normal_contained_in': ['2.g1', '2.i1', '2.j1'], 'normal_contains': ['8.p1', '8.u1', '8.u2', '8.w1', '8.y1', '8.bh1', '8.bh2'], 'normalizer': '1.a1', 'old_label': '4.bd1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bd1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063555
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.be1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.ba1', '64.bd1', '64.bb1'], 'conjugacy_class_count': 8, 'contained_in': ['2.f1', '2.k1'], 'contains': ['8.q1', '8.r1', '8.t1', '8.z1', '8.ba1', '8.bd1', '8.bg1'], 'core': '4.be1', 'coset_action_label': None, 'count': 8, 'diagramx': [1756, 1368, 1750, 1368], 'generators': [1, 18, 212], 'label': '256.29702.4.be1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.be1', 'normal_contained_in': ['2.f1', '2.k1'], 'normal_contains': ['8.q1', '8.r1', '8.t1', '8.z1', '8.ba1', '8.bd1', '8.bg1'], 'normalizer': '1.a1', 'old_label': '4.be1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.be1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063556
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.bf1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.be1', '64.ba1', '64.bd1', '64.bb1'], 'conjugacy_class_count': 4, 'contained_in': ['2.g1', '2.k1'], 'contains': ['8.q1', '8.u1', '8.ba1', '8.bb1', '8.bh1'], 'core': '4.bf1', 'coset_action_label': None, 'count': 4, 'diagramx': [1635, 3198, 1629, 3197], 'generators': [5, 18, 212], 'label': '256.29702.4.bf1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bf1', 'normal_contained_in': ['2.g1', '2.k1'], 'normal_contains': ['8.q1', '8.u1', '8.ba1', '8.bb1', '8.bh1'], 'normalizer': '1.a1', 'old_label': '4.bf1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bf1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063557
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.bf2', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.bd1', '64.bb1', '64.ba1', '64.be1'], 'conjugacy_class_count': 4, 'contained_in': ['2.g1', '2.k1'], 'contains': ['8.q1', '8.u2', '8.ba1', '8.bb1', '8.bh2', '8.cf1'], 'core': '4.bf2', 'coset_action_label': None, 'count': 4, 'diagramx': [1178, 2911, 1173, 2910], 'generators': [21, 18, 212, 128], 'label': '256.29702.4.bf2', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bf2', 'normal_contained_in': ['2.g1', '2.k1'], 'normal_contains': ['8.q1', '8.u2', '8.ba1', '8.bb1', '8.bh2'], 'normalizer': '1.a1', 'old_label': '4.bf2', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bf2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063558
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.bg1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.ba1', '64.bb1', '64.bc1', '64.bd1'], 'conjugacy_class_count': 8, 'contained_in': ['2.h1', '2.i1', '2.k1'], 'contains': ['8.r1', '8.s1', '8.u2', '8.bc1', '8.bd1', '8.be1', '8.bh1'], 'core': '4.bg1', 'coset_action_label': None, 'count': 8, 'diagramx': [2288, 731, 2281, 731], 'generators': [1, 18, 80], 'label': '256.29702.4.bg1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bg1', 'normal_contained_in': ['2.h1', '2.i1', '2.k1'], 'normal_contains': ['8.r1', '8.s1', '8.u2', '8.bc1', '8.bd1', '8.be1', '8.bh1'], 'normalizer': '1.a1', 'old_label': '4.bg1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bg1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063559
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.bg2', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.ba1', '64.bb1', '64.bc1', '64.bd1'], 'conjugacy_class_count': 8, 'contained_in': ['2.h1', '2.i1', '2.k1'], 'contains': ['8.r1', '8.s1', '8.u1', '8.bc1', '8.bd1', '8.be2', '8.bh2'], 'core': '4.bg2', 'coset_action_label': None, 'count': 8, 'diagramx': [2106, 994, 2099, 994], 'generators': [1, 18, 64], 'label': '256.29702.4.bg2', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bg2', 'normal_contained_in': ['2.h1', '2.i1', '2.k1'], 'normal_contains': ['8.r1', '8.s1', '8.u1', '8.bc1', '8.bd1', '8.be2', '8.bh2'], 'normalizer': '1.a1', 'old_label': '4.bg2', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bg2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063560
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.bh1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.be1', '64.ba1', '64.bb1', '64.bc1', '64.bd1'], 'conjugacy_class_count': 8, 'contained_in': ['2.h1', '2.j1', '2.k1'], 'contains': ['8.s1', '8.t1', '8.u1', '8.be1', '8.bf1', '8.bg1', '8.bh2'], 'core': '4.bh1', 'coset_action_label': None, 'count': 8, 'diagramx': [2729, 101, 2720, 101], 'generators': [5, 18, 80], 'label': '256.29702.4.bh1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bh1', 'normal_contained_in': ['2.h1', '2.j1', '2.k1'], 'normal_contains': ['8.s1', '8.t1', '8.u1', '8.be1', '8.bf1', '8.bg1', '8.bh2'], 'normalizer': '1.a1', 'old_label': '4.bh1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bh1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063561
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '4.bh2', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': ['64.bd1', '64.ba1', '64.bb1', '64.bc1', '64.be1'], 'conjugacy_class_count': 8, 'contained_in': ['2.h1', '2.j1', '2.k1'], 'contains': ['8.s1', '8.t1', '8.u2', '8.be2', '8.bf1', '8.bg1', '8.bh1'], 'core': '4.bh2', 'coset_action_label': None, 'count': 8, 'diagramx': [3084, 315, 3075, 315], 'generators': [17, 18, 64], 'label': '256.29702.4.bh2', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bh2', 'normal_contained_in': ['2.h1', '2.j1', '2.k1'], 'normal_contains': ['8.s1', '8.t1', '8.u2', '8.be2', '8.bf1', '8.bg1', '8.bh1'], 'normalizer': '1.a1', 'old_label': '4.bh2', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bh2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063562
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.b1', 'complements': ['128.f1', '128.i1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.d1', '4.k1', '4.o1', '4.v1', '4.y1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4689, 6985, 4675, 6982], 'generators': [2, 4, 16, 64], 'label': '256.29702.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.d1', '4.k1', '4.o1', '4.v1', '4.y1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063563
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '4.bi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': None, 'aut_weyl_index': 128, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.a1'], 'contains': ['8.bi1', '8.bo1', '8.bq1', '8.br1', '8.bs1', '8.bw1', '8.bx1'], 'core': '8.bi1', 'coset_action_label': None, 'count': 16, 'diagramx': [5751, -1, 5734, -1], 'generators': [1, 2, 4, 64], 'label': '256.29702.4.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.bi1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063564
    {'ambient': '256.29702', 'aut_centralizer_order': 16, 'aut_label': '4.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': None, 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.c1'], 'contains': ['8.bi1', '8.bp1', '8.bt1', '8.bu1', '8.bv1', '8.by1', '8.bz1', '8.ca1'], 'core': '8.bi1', 'coset_action_label': None, 'count': 16, 'diagramx': [9193, -1, 9167, -1], 'generators': [17, 2, 4, 64], 'label': '256.29702.4.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.bj1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bj1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063565
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '512.418986', 'aut_weyl_index': 512, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.b1', '16.l1', '16.q1', '16.cb1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5801, 8618, 5785, 8616], 'generators': [2, 4, 8, 128, 160], 'label': '256.29702.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.b1', '16.l1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063566
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.b1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.f1', '4.g1', '4.h1', '4.i1'], 'contains': ['16.a1', '16.c1', '16.r1', '16.bf1', '16.cc1', '16.cc2'], 'core': '8.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [856, 7907, 854, 7904], 'generators': [1, 2, 8, 128, 160], 'label': '256.29702.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.f1', '4.g1', '4.h1', '4.i1'], 'normal_contains': ['16.a1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063567
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.c1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '512.254238', 'aut_weyl_index': 512, 'centralizer': '8.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.f1', '4.j1', '4.k1', '4.l1'], 'contains': ['16.a1', '16.d1', '16.e1', '16.m1', '16.s1', '16.cd1'], 'core': '8.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6959, 8496, 6940, 8494], 'generators': [2, 196, 8, 128, 160], 'label': '256.29702.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.f1', '4.j1', '4.k1', '4.l1'], 'normal_contains': ['16.a1', '16.d1', '16.e1', '16.m1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063568
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.d1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '256.1529', 'aut_weyl_index': 1024, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.g1', '4.j1', '4.m1', '4.n1'], 'contains': ['16.a1', '16.f1', '16.j1', '16.t1', '16.bg1'], 'core': '8.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [7535, 7449, 7514, 7447], 'generators': [17, 2, 8, 160], 'label': '256.29702.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.c1', '4.g1', '4.j1', '4.m1', '4.n1'], 'normal_contains': ['16.a1', '16.f1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063569
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.e1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '512.418986', 'aut_weyl_index': 512, 'centralizer': '8.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.h1', '4.m1', '4.o1'], 'contains': ['16.a1', '16.g1', '16.n1', '16.u1'], 'core': '8.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [7698, 8318, 7677, 8316], 'generators': [2, 64, 8, 160], 'label': '256.29702.8.e1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1', 'normal_contained_in': ['4.b1', '4.h1', '4.m1', '4.o1'], 'normal_contains': ['16.a1', '16.g1', '16.n1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063570
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '16.g1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.g1', '4.i1', '4.k1', '4.n1', '4.o1', '4.p1'], 'contains': ['16.a1', '16.h1', '16.v1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [3873, 7192, 3863, 7190], 'generators': [2, 80, 8], 'label': '256.29702.8.f1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': ['4.d1', '4.g1', '4.i1', '4.k1', '4.n1', '4.o1', '4.p1'], 'normal_contains': ['16.a1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063571
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.g1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '8.g1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '4.f1', '4.h1', '4.n1', '4.p1'], 'contains': ['16.a1', '16.i1', '16.bh1', '16.ce1'], 'core': '8.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [4583, 8085, 4570, 8082], 'generators': [65, 2, 160, 128], 'label': '256.29702.8.g1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': ['4.e1', '4.f1', '4.h1', '4.n1', '4.p1'], 'normal_contains': ['16.a1', '16.i1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063572
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.h1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '256.5675', 'aut_weyl_index': 1024, 'centralizer': '16.e1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.i1', '4.l1', '4.m1', '4.p1'], 'contains': ['16.a1', '16.k1', '16.bi1'], 'core': '8.h1', 'coset_action_label': None, 'count': 2, 'diagramx': [6462, 7706, 6444, 7704], 'generators': [81, 2, 160], 'label': '256.29702.8.h1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1', 'normal_contained_in': ['4.c1', '4.i1', '4.l1', '4.m1', '4.p1'], 'normal_contains': ['16.a1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063573
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 16, 'centralizer': '32.b1', 'complements': ['128.g1', '128.h1', '128.i1', '128.f1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '4.e1', '4.n1', '4.p1', '4.z1', '4.ba1'], 'core': '2.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [3909, 6786, 3897, 6783], 'generators': [17, 2, 4, 80], 'label': '256.29702.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1', '4.e1', '4.n1', '4.p1', '4.z1', '4.ba1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063574
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.i1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.q1', '4.r1', '4.s1', '4.t1'], 'contains': ['16.b1', '16.c1', '16.w1', '16.w2', '16.bj1', '16.cf1', '16.cf2'], 'core': '8.i1', 'coset_action_label': None, 'count': 4, 'diagramx': [383, 3859, 381, 3858], 'generators': [1, 6, 8, 128, 160], 'label': '256.29702.8.i1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1', 'normal_contained_in': ['4.a1', '4.q1', '4.r1', '4.s1', '4.t1'], 'normal_contains': ['16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.i1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063575
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.j1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 1024, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.q1', '4.u1', '4.v1', '4.w1'], 'contains': ['16.b1', '16.d1', '16.g1', '16.o1', '16.x1', '16.x2'], 'core': '8.j1', 'coset_action_label': None, 'count': 2, 'diagramx': [7861, 6700, 7839, 6698], 'generators': [6, 196, 8, 160], 'label': '256.29702.8.j1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1', 'normal_contained_in': ['4.b1', '4.q1', '4.u1', '4.v1', '4.w1'], 'normal_contains': ['16.b1', '16.d1', '16.g1', '16.o1'], 'normalizer': '1.a1', 'old_label': '8.j1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063576
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.k1', 'aut_quo_index': 42, 'aut_stab_index': 2, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 1024, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.r1', '4.x1', '4.y1'], 'contains': ['16.b1', '16.e1', '16.g1', '16.p1', '16.y1', '16.y2'], 'core': '8.k1', 'coset_action_label': None, 'count': 2, 'diagramx': [6836, 6934, 6816, 6933], 'generators': [6, 64, 8, 160], 'label': '256.29702.8.k1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1', 'normal_contained_in': ['4.b1', '4.r1', '4.x1', '4.y1'], 'normal_contains': ['16.b1', '16.e1', '16.g1', '16.p1'], 'normalizer': '1.a1', 'old_label': '8.k1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063577
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.l1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '4.s1', '4.u1', '4.x1', '4.z1'], 'contains': ['16.b1', '16.f1', '16.k1', '16.bk1', '16.cg1'], 'core': '8.l1', 'coset_action_label': None, 'count': 4, 'diagramx': [6089, 6343, 6072, 6341], 'generators': [81, 6, 160, 128], 'label': '256.29702.8.l1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1', 'normal_contained_in': ['4.c1', '4.s1', '4.u1', '4.x1', '4.z1'], 'normal_contains': ['16.b1', '16.f1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.l1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063578
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.m1', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['4.d1', '4.s1', '4.t1', '4.v1', '4.y1', '4.z1', '4.ba1'], 'contains': ['16.b1', '16.h1', '16.ch1'], 'core': '8.m1', 'coset_action_label': None, 'count': 8, 'diagramx': [2301, 3379, 2294, 3378], 'generators': [6, 80, 128], 'label': '256.29702.8.m1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.m1', 'normal_contained_in': ['4.d1', '4.s1', '4.t1', '4.v1', '4.y1', '4.z1', '4.ba1'], 'normal_contains': ['16.b1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.m1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063579
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.n1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.e1', '4.q1', '4.r1', '4.z1', '4.ba1'], 'contains': ['16.b1', '16.i1', '16.bl1'], 'core': '8.n1', 'coset_action_label': None, 'count': 4, 'diagramx': [4242, 4544, 4230, 4542], 'generators': [65, 6, 160], 'label': '256.29702.8.n1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.n1', 'normal_contained_in': ['4.e1', '4.q1', '4.r1', '4.z1', '4.ba1'], 'normal_contains': ['16.b1', '16.i1'], 'normalizer': '1.a1', 'old_label': '8.n1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063580
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.o1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '4.t1', '4.w1', '4.x1', '4.ba1'], 'contains': ['16.b1', '16.j1', '16.k1', '16.bm1'], 'core': '8.o1', 'coset_action_label': None, 'count': 4, 'diagramx': [6268, 4823, 6250, 4822], 'generators': [17, 6, 160], 'label': '256.29702.8.o1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.o1', 'normal_contained_in': ['4.c1', '4.t1', '4.w1', '4.x1', '4.ba1'], 'normal_contains': ['16.b1', '16.j1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.o1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063581
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.p1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 2048, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '4.q1', '4.bb1', '4.bc1', '4.bd1'], 'contains': ['16.c1', '16.d1', '16.i1', '16.bn1', '16.ci1', '16.ci2'], 'core': '8.p1', 'coset_action_label': None, 'count': 4, 'diagramx': [3188, 3122, 3179, 3121], 'generators': [1, 196, 160, 128], 'label': '256.29702.8.p1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.p1', 'normal_contained_in': ['4.f1', '4.q1', '4.bb1', '4.bc1', '4.bd1'], 'normal_contains': ['16.c1', '16.d1', '16.i1'], 'normalizer': '1.a1', 'old_label': '8.p1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063582
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.q1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 2048, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '4.r1', '4.be1', '4.bf1', '4.bf2'], 'contains': ['16.c1', '16.e1', '16.i1', '16.bo1', '16.cj1', '16.cj2'], 'core': '8.q1', 'coset_action_label': None, 'count': 4, 'diagramx': [2907, 4037, 2899, 4036], 'generators': [1, 198, 160, 128], 'label': '256.29702.8.q1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.q1', 'normal_contained_in': ['4.f1', '4.r1', '4.be1', '4.bf1', '4.bf2'], 'normal_contains': ['16.c1', '16.e1', '16.i1'], 'normalizer': '1.a1', 'old_label': '8.q1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063583
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.r1', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['4.g1', '4.s1', '4.bb1', '4.be1', '4.bg1', '4.bg2'], 'contains': ['16.c1', '16.f1', '16.h1', '16.z1', '16.ck1', '16.ck2'], 'core': '8.r1', 'coset_action_label': None, 'count': 8, 'diagramx': [1185, 1429, 1181, 1429], 'generators': [7, 80, 8, 128], 'label': '256.29702.8.r1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.r1', 'normal_contained_in': ['4.g1', '4.s1', '4.bb1', '4.be1', '4.bg1', '4.bg2'], 'normal_contains': ['16.c1', '16.f1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.r1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063584
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 16, 'centralizer': '32.b1', 'complements': ['128.f1', '128.e1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.f1', '4.g1', '4.j1', '4.k1', '4.n1', '4.bb1', '4.bc1', '4.be1'], 'core': '2.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [3347, 6189, 3332, 6185], 'generators': [17, 2, 20, 80], 'label': '256.29702.2.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.f1', '4.g1', '4.j1', '4.k1', '4.n1', '4.bb1', '4.bc1', '4.be1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063585
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.s1', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['4.h1', '4.q1', '4.r1', '4.bg1', '4.bg2', '4.bh1', '4.bh2'], 'contains': ['16.c1', '16.g1', '16.i1', '16.bp1'], 'core': '8.s1', 'coset_action_label': None, 'count': 8, 'diagramx': [3679, 1172, 3669, 1172], 'generators': [1, 64, 160], 'label': '256.29702.8.s1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.s1', 'normal_contained_in': ['4.h1', '4.q1', '4.r1', '4.bg1', '4.bg2', '4.bh1', '4.bh2'], 'normal_contains': ['16.c1', '16.g1', '16.i1'], 'normalizer': '1.a1', 'old_label': '8.s1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063586
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.t1', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['4.g1', '4.t1', '4.bc1', '4.be1', '4.bh1', '4.bh2'], 'contains': ['16.c1', '16.h1', '16.j1', '16.ba1'], 'core': '8.t1', 'coset_action_label': None, 'count': 8, 'diagramx': [1543, 165, 1539, 165], 'generators': [5, 80, 8], 'label': '256.29702.8.t1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.t1', 'normal_contained_in': ['4.g1', '4.t1', '4.bc1', '4.be1', '4.bh1', '4.bh2'], 'normal_contains': ['16.c1', '16.h1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.t1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063587
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.u1', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['4.i1', '4.s1', '4.t1', '4.bd1', '4.bf1', '4.bg2', '4.bh1'], 'contains': ['16.c1', '16.h1', '16.k1', '16.cl1'], 'core': '8.u1', 'coset_action_label': None, 'count': 8, 'diagramx': [522, 893, 521, 893], 'generators': [3, 80, 128], 'label': '256.29702.8.u1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.u1', 'normal_contained_in': ['4.i1', '4.s1', '4.t1', '4.bd1', '4.bf1', '4.bg2', '4.bh1'], 'normal_contains': ['16.c1', '16.h1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.u1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063588
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.u2', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 8, 'contained_in': ['4.i1', '4.s1', '4.t1', '4.bd1', '4.bf2', '4.bg1', '4.bh2'], 'contains': ['16.c1', '16.h1', '16.k1', '16.cl2'], 'core': '8.u2', 'coset_action_label': None, 'count': 8, 'diagramx': [717, 614, 714, 613], 'generators': [1, 80, 128], 'label': '256.29702.8.u2', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.u2', 'normal_contained_in': ['4.i1', '4.s1', '4.t1', '4.bd1', '4.bf2', '4.bg1', '4.bh2'], 'normal_contains': ['16.c1', '16.h1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.u2', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063589
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.v1', 'aut_quo_index': 21, 'aut_stab_index': 1, 'aut_weyl_group': '512.51574', 'aut_weyl_index': 512, 'centralizer': '8.v1', 'complements': ['32.cf1'], 'conjugacy_class_count': 1, 'contained_in': ['4.j1', '4.u1', '4.bb1'], 'contains': ['16.d1', '16.f1', '16.bb1', '16.bq1', '16.cm1'], 'core': '8.v1', 'coset_action_label': None, 'count': 1, 'diagramx': [7239, 6521, 7218, 6520], 'generators': [19, 196, 8, 128, 160], 'label': '256.29702.8.v1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.v1', 'normal_contained_in': ['4.j1', '4.u1', '4.bb1'], 'normal_contains': ['16.d1', '16.f1'], 'normalizer': '1.a1', 'old_label': '8.v1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.v1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063590
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.w1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': ['32.cf1'], 'conjugacy_class_count': 4, 'contained_in': ['4.k1', '4.v1', '4.bb1', '4.bc1', '4.bd1'], 'contains': ['16.d1', '16.h1', '16.cn1'], 'core': '8.w1', 'coset_action_label': None, 'count': 4, 'diagramx': [3484, 2865, 3475, 2864], 'generators': [18, 196, 128], 'label': '256.29702.8.w1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.w1', 'normal_contained_in': ['4.k1', '4.v1', '4.bb1', '4.bc1', '4.bd1'], 'normal_contains': ['16.d1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.w1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.w1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063591
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.x1', 'aut_quo_index': 21, 'aut_stab_index': 1, 'aut_weyl_group': '512.51574', 'aut_weyl_index': 512, 'centralizer': '8.x1', 'complements': ['32.cf1'], 'conjugacy_class_count': 1, 'contained_in': ['4.j1', '4.w1', '4.bc1'], 'contains': ['16.d1', '16.j1', '16.bc1', '16.br1'], 'core': '8.x1', 'coset_action_label': None, 'count': 1, 'diagramx': [8352, 5359, 8329, 5358], 'generators': [17, 196, 8, 160], 'label': '256.29702.8.x1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.x1', 'normal_contained_in': ['4.j1', '4.w1', '4.bc1'], 'normal_contains': ['16.d1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.x1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.x1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063592
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.y1', 'aut_quo_index': 42, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '16.e1', 'complements': ['32.cf1'], 'conjugacy_class_count': 2, 'contained_in': ['4.l1', '4.u1', '4.w1', '4.bd1'], 'contains': ['16.d1', '16.k1', '16.bs1'], 'core': '8.y1', 'coset_action_label': None, 'count': 2, 'diagramx': [7098, 6086, 7079, 6084], 'generators': [21, 196, 160], 'label': '256.29702.8.y1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.y1', 'normal_contained_in': ['4.l1', '4.u1', '4.w1', '4.bd1'], 'normal_contains': ['16.d1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.y1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.y1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063593
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.z1', 'aut_quo_index': 42, 'aut_stab_index': 2, 'aut_weyl_group': '256.1529', 'aut_weyl_index': 1024, 'centralizer': '16.d1', 'complements': ['32.cf1'], 'conjugacy_class_count': 2, 'contained_in': ['4.j1', '4.x1', '4.be1'], 'contains': ['16.e1', '16.f1', '16.j1', '16.bd1', '16.bt1'], 'core': '8.z1', 'coset_action_label': None, 'count': 2, 'diagramx': [8025, 5595, 8003, 5593], 'generators': [17, 198, 8, 160], 'label': '256.29702.8.z1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.z1', 'normal_contained_in': ['4.j1', '4.x1', '4.be1'], 'normal_contains': ['16.e1', '16.f1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.z1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.z1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063594
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.ba1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': ['32.cf1'], 'conjugacy_class_count': 4, 'contained_in': ['4.k1', '4.y1', '4.be1', '4.bf1', '4.bf2'], 'contains': ['16.e1', '16.h1', '16.co1'], 'core': '8.ba1', 'coset_action_label': None, 'count': 4, 'diagramx': [1738, 3658, 1733, 3657], 'generators': [18, 212, 128], 'label': '256.29702.8.ba1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ba1', 'normal_contained_in': ['4.k1', '4.y1', '4.be1', '4.bf1', '4.bf2'], 'normal_contains': ['16.e1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.ba1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ba1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063595
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '32.b1', 'complements': ['128.i1', '128.e1', '128.f1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.f1', '4.i1', '4.k1', '4.l1', '4.p1', '4.bd1', '4.bf1', '4.bf2'], 'core': '2.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [2820, 6388, 2820, 6384], 'generators': [1, 2, 20, 80], 'label': '256.29702.2.g1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.f1', '4.i1', '4.k1', '4.l1', '4.p1', '4.bd1', '4.bf1', '4.bf2'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063596
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.bb1', 'aut_quo_index': 42, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '8.bb1', 'complements': ['32.cf1'], 'conjugacy_class_count': 2, 'contained_in': ['4.l1', '4.x1', '4.bf1', '4.bf2'], 'contains': ['16.e1', '16.k1', '16.bu1', '16.cp1'], 'core': '8.bb1', 'coset_action_label': None, 'count': 2, 'diagramx': [5926, 5829, 5909, 5827], 'generators': [21, 198, 160, 128], 'label': '256.29702.8.bb1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bb1', 'normal_contained_in': ['4.l1', '4.x1', '4.bf1', '4.bf2'], 'normal_contains': ['16.e1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.bb1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.bb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063597
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.bc1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': ['32.cf1'], 'conjugacy_class_count': 4, 'contained_in': ['4.m1', '4.u1', '4.x1', '4.bg1', '4.bg2'], 'contains': ['16.f1', '16.g1', '16.k1', '16.bv1'], 'core': '8.bc1', 'coset_action_label': None, 'count': 4, 'diagramx': [6657, 5103, 6638, 5101], 'generators': [19, 64, 160], 'label': '256.29702.8.bc1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bc1', 'normal_contained_in': ['4.m1', '4.u1', '4.x1', '4.bg1', '4.bg2'], 'normal_contains': ['16.f1', '16.g1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.bc1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.bc1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063598
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.bd1', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': ['32.cf1'], 'conjugacy_class_count': 8, 'contained_in': ['4.n1', '4.z1', '4.bb1', '4.be1', '4.bg1', '4.bg2'], 'contains': ['16.f1', '16.h1', '16.i1', '16.cq1'], 'core': '8.bd1', 'coset_action_label': None, 'count': 8, 'diagramx': [2106, 1686, 2100, 1686], 'generators': [19, 80, 128], 'label': '256.29702.8.bd1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bd1', 'normal_contained_in': ['4.n1', '4.z1', '4.bb1', '4.be1', '4.bg1', '4.bg2'], 'normal_contains': ['16.f1', '16.h1', '16.i1'], 'normalizer': '1.a1', 'old_label': '8.bd1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.bd1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063599
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.be1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '16.g1', 'complements': ['32.cf1'], 'conjugacy_class_count': 4, 'contained_in': ['4.o1', '4.v1', '4.y1', '4.bg1', '4.bh1'], 'contains': ['16.g1', '16.h1', '16.be1'], 'core': '8.be1', 'coset_action_label': None, 'count': 4, 'diagramx': [4058, 2367, 4046, 2366], 'generators': [18, 80, 8], 'label': '256.29702.8.be1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.be1', 'normal_contained_in': ['4.o1', '4.v1', '4.y1', '4.bg1', '4.bh1'], 'normal_contains': ['16.g1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.be1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.be1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063600
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.be2', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '8.be2', 'complements': ['32.cf1'], 'conjugacy_class_count': 4, 'contained_in': ['4.o1', '4.v1', '4.y1', '4.bg2', '4.bh2'], 'contains': ['16.g1', '16.h1', '16.be2'], 'core': '8.be2', 'coset_action_label': None, 'count': 4, 'diagramx': [4420, 2607, 4408, 2607], 'generators': [18, 64, 8], 'label': '256.29702.8.be2', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.be2', 'normal_contained_in': ['4.o1', '4.v1', '4.y1', '4.bg2', '4.bh2'], 'normal_contains': ['16.g1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.be2', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.be2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063601
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.bf1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': ['32.cf1'], 'conjugacy_class_count': 4, 'contained_in': ['4.m1', '4.w1', '4.x1', '4.bh1', '4.bh2'], 'contains': ['16.g1', '16.j1', '16.k1', '16.bw1'], 'core': '8.bf1', 'coset_action_label': None, 'count': 4, 'diagramx': [7366, 4279, 7346, 4278], 'generators': [17, 64, 160], 'label': '256.29702.8.bf1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bf1', 'normal_contained_in': ['4.m1', '4.w1', '4.x1', '4.bh1', '4.bh2'], 'normal_contains': ['16.g1', '16.j1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.bf1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.bf1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063602
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.bg1', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': ['32.cf1'], 'conjugacy_class_count': 8, 'contained_in': ['4.n1', '4.ba1', '4.bc1', '4.be1', '4.bh1', '4.bh2'], 'contains': ['16.h1', '16.i1', '16.j1'], 'core': '8.bg1', 'coset_action_label': None, 'count': 8, 'diagramx': [3329, 389, 3319, 389], 'generators': [17, 80], 'label': '256.29702.8.bg1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bg1', 'normal_contained_in': ['4.n1', '4.ba1', '4.bc1', '4.be1', '4.bh1', '4.bh2'], 'normal_contains': ['16.h1', '16.i1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.bg1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.bg1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063603
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.bh1', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': ['32.cf1'], 'conjugacy_class_count': 8, 'contained_in': ['4.p1', '4.z1', '4.ba1', '4.bd1', '4.bf1', '4.bg1', '4.bh2'], 'contains': ['16.h1', '16.i1', '16.k1'], 'core': '8.bh1', 'coset_action_label': None, 'count': 8, 'diagramx': [3048, 2159, 3039, 2158], 'generators': [21, 80], 'label': '256.29702.8.bh1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bh1', 'normal_contained_in': ['4.p1', '4.z1', '4.ba1', '4.bd1', '4.bf1', '4.bg1', '4.bh2'], 'normal_contains': ['16.h1', '16.i1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.bh1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.bh1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063604
    {'ambient': '256.29702', 'aut_centralizer_order': 512, 'aut_label': '8.bh2', 'aut_quo_index': 168, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 4096, 'centralizer': '32.b1', 'complements': ['32.cf1'], 'conjugacy_class_count': 8, 'contained_in': ['4.p1', '4.z1', '4.ba1', '4.bd1', '4.bf2', '4.bg2', '4.bh1'], 'contains': ['16.h1', '16.i1', '16.k1', '16.cr1'], 'core': '8.bh2', 'coset_action_label': None, 'count': 8, 'diagramx': [1922, 1951, 1916, 1950], 'generators': [23, 80, 128], 'label': '256.29702.8.bh2', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bh2', 'normal_contained_in': ['4.p1', '4.z1', '4.ba1', '4.bd1', '4.bf2', '4.bg2', '4.bh1'], 'normal_contains': ['16.h1', '16.i1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.bh2', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.bh2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063605
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.bi1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '16.a1', 'complements': ['32.bk1'], 'conjugacy_class_count': 8, 'contained_in': ['4.b1', '4.bi1', '4.bj1'], 'contains': ['16.l1', '16.m1', '16.n1', '16.o1', '16.p1', '16.by1'], 'core': '8.bi1', 'coset_action_label': None, 'count': 8, 'diagramx': [8678, 8797, 8654, 8794], 'generators': [2, 4, 64, 8], 'label': '256.29702.8.bi1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.bi1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.l1', '16.m1', '16.n1', '16.o1', '16.p1'], 'normalizer': '1.a1', 'old_label': '8.bi1', 'projective_image': '64.261', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.bi1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063606
    {'ambient': '256.29702', 'aut_centralizer_order': 8, 'aut_label': '2.h1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 32, 'centralizer': '32.b1', 'complements': ['128.i1', '128.e1', '128.f1', '128.g1', '128.h1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.g1', '4.h1', '4.i1', '4.m1', '4.n1', '4.o1', '4.p1', '4.bg1', '4.bg2', '4.bh1', '4.bh2'], 'core': '2.h1', 'coset_action_label': None, 'count': 4, 'diagramx': [3134, 5990, 3113, 5986], 'generators': [1, 2, 20, 64], 'label': '256.29702.2.h1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.g1', '4.h1', '4.i1', '4.m1', '4.n1', '4.o1', '4.p1', '4.bg1', '4.bg2', '4.bh1', '4.bh2'], 'normalizer': '1.a1', 'old_label': '2.h1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.h1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 30063607
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1'], 'contains': ['16.q1', '16.r1', '16.w1', '16.w2', '16.bx1', '16.ca1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [297, -1, 297, -1], 'generators': [1, 2, 4, 128, 160], 'label': '256.29702.8.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '8.bj1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 30063608
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.bk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1'], 'contains': ['16.q1', '16.s1', '16.u1', '16.x1', '16.x2', '16.y1', '16.y2', '16.by1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8188, -1, 8165, -1], 'generators': [2, 4, 64, 160], 'label': '256.29702.8.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '8.bk1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063609
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.g1'], 'contains': ['16.r1', '16.t1', '16.v1', '16.z1', '16.ba1'], 'core': '32.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2735, -1, 2728, -1], 'generators': [5, 2, 80], 'label': '256.29702.8.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '8.bl1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063610
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '16.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.j1'], 'contains': ['16.s1', '16.t1', '16.bb1', '16.bc1', '16.bd1', '16.bz1'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8515, -1, 8491, -1], 'generators': [17, 2, 196, 160], 'label': '256.29702.8.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1', 'old_label': '8.bm1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063611
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 1024, 'centralizer': '16.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.o1'], 'contains': ['16.u1', '16.v1', '16.be1', '16.be2'], 'core': '32.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4755, -1, 4742, -1], 'generators': [2, 20, 64], 'label': '256.29702.8.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1', 'old_label': '8.bn1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 30063612
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '512.51562', 'aut_weyl_index': 512, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.bi1'], 'contains': ['16.l1', '16.bf1', '16.bj1', '16.bx1', '16.cs1'], 'core': '16.l1', 'coset_action_label': None, 'count': 8, 'diagramx': [2440, -1, 2433, -1], 'generators': [1, 2, 4, 128, 8], 'label': '256.29702.8.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bo1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 30063613
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.bp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 2048, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.c1', '4.bj1'], 'contains': ['16.l1', '16.bg1', '16.bi1', '16.bk1', '16.bm1'], 'core': '16.l1', 'coset_action_label': None, 'count': 16, 'diagramx': [9044, -1, 9019, -1], 'generators': [17, 2, 4], 'label': '256.29702.8.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bp1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bp1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 30063614
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.bq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '512.51562', 'aut_weyl_index': 512, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.e1', '4.bi1'], 'contains': ['16.l1', '16.bh1', '16.bl1'], 'core': '16.l1', 'coset_action_label': None, 'count': 8, 'diagramx': [5662, -1, 5646, -1], 'generators': [65, 2, 4], 'label': '256.29702.8.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bq1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063615
    {'ambient': '256.29702', 'aut_centralizer_order': 128, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 2048, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.f1', '4.bi1'], 'contains': ['16.m1', '16.bf1', '16.bh1', '16.bn1', '16.bo1', '16.ct1'], 'core': '16.m1', 'coset_action_label': None, 'count': 16, 'diagramx': [4929, -1, 4915, -1], 'generators': [1, 2, 196, 128], 'label': '256.29702.8.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.br1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 30063616
    {'ambient': '256.29702', 'aut_centralizer_order': 64, 'aut_label': '8.bs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '256.8935', 'aut_weyl_index': 1024, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.h1', '4.bi1'], 'contains': ['16.n1', '16.bf1', '16.bh1', '16.bp1'], 'core': '16.n1', 'coset_action_label': None, 'count': 16, 'diagramx': [5467, -1, 5452, -1], 'generators': [1, 2, 64], 'label': '256.29702.8.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bs1', 'projective_image': '64.261', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}