Abstract group data - 256.26547

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [4, 4, 4, 2, 4, 8, 4, 4], 'aut_gens': [[1, 2, 8, 32, 64], [97, 18, 8, 32, 64], [41, 170, 136, 32, 64], [185, 186, 8, 160, 64], [1, 118, 8, 176, 208], [157, 30, 200, 160, 192], [41, 238, 24, 48, 80], [241, 162, 152, 160, 192], [101, 162, 72, 176, 208]], 'aut_group': '4096.btn', 'aut_hash': 929749695181227092, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 48, 'aut_perms': [11652553905134116822778022631217506370009747833909296541781094, 2489950937434609929069820821789348110067534387294262421369440, 4146117624189865395322292468375820660106226063798617107325839, 149096292540385108498814255282012865382286514235962192237976, 9577382745753629202579244759234188008707420106193681494485143, 2466643156370600873320361521723740306305094566616592395927917, 2918487816831413146642662873485112037339560962969087752773419, 8811136701353823791350534366904320703661445040517894872493649], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 4, 2, 1], [2, 8, 1, 1], [2, 8, 2, 1], [2, 8, 4, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 4, 2, 2], [4, 8, 1, 2], [4, 8, 2, 1], [4, 8, 4, 1], [4, 16, 4, 1], [8, 16, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4.D_4^2:C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '256.53380', 'autcentquo_hash': 53380, 'autcentquo_nilpotent': True, 'autcentquo_order': 256, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^5:D_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 3], [2, 8, 7], [4, 2, 2], [4, 4, 5], [4, 8, 8], [4, 16, 4], [8, 16, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '128.1755', 'commutator_count': 1, 'commutator_label': '16.11', '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': 26547, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 3], [2, 8, 1, 7], [4, 2, 1, 2], [4, 4, 1, 5], [4, 8, 1, 8], [4, 16, 1, 4], [8, 16, 1, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 322560, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 1, 2]], 'familial': False, 'frattini_label': '16.11', 'frattini_quotient': '16.14', 'hash': 26547, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4, 4, 2, 2], 'inner_gens': [[1, 6, 8, 48, 208], [5, 2, 216, 176, 80], [1, 82, 8, 32, 64], [17, 146, 8, 32, 64], [145, 18, 8, 32, 64]], 'inner_hash': 1755, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': False, 'inner_tex': 'C_2^4:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 12], [4, 4], [8, 2]], 'label': '256.26547', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'D4^2:C2^2', 'ngens': 4, 'nilpotency_class': 4, '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': 19, 'number_characteristic_subgroups': 29, 'number_conjugacy_classes': 34, 'number_divisions': 34, 'number_normal_subgroups': 109, 'number_subgroup_autclasses': 274, 'number_subgroup_classes': 624, 'number_subgroups': 2079, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 71], [4, 152], [8, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2], 'outer_gen_pows': [192, 224, 16, 0, 0], 'outer_gens': [[217, 10, 8, 32, 64], [225, 226, 8, 32, 64], [17, 226, 8, 32, 64], [1, 2, 8, 160, 64], [1, 2, 136, 32, 64]], 'outer_group': '32.51', 'outer_hash': 51, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 32, 'outer_perms': [8259470424175296574426514081379841, 17774154876782283574170730336362004, 26330869002213901050922466899460658, 34830753587784208264754691194221536, 43328107513216344878530623767946840], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 4], [8, 2]], 'representations': {'PC': {'code': 2733226370113958205152517009651537516746, 'gens': [1, 2, 4, 6, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 97, 41, 3467, 211, 91, 2892, 2309, 4237, 1941, 11654, 2254, 2710, 166]}, 'Perm': {'d': 16, 'gens': [11212821043200, 1307714313462, 5612462150273, 8402254554953, 5606234750016, 2789832700823, 5167, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_4^2:C_2^2', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 109447089
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 26547, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 109447100
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 26547, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
  • id: 109447111
    {'aut_label': '2B', 'centralizer': '2.c1', 'counter': 3, 'group_counter': 26547, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 16, 'size': 2}
  • id: 109447117
    {'aut_label': '2C', 'centralizer': '4.s1', 'counter': 4, 'group_counter': 26547, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 32, 'size': 4}
  • id: 109447118
    {'aut_label': '2D', 'centralizer': '4.u1', 'counter': 5, 'group_counter': 26547, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 4, 'size': 4}
  • id: 109447119
    {'aut_label': '2D', 'centralizer': '4.u1', 'counter': 6, 'group_counter': 26547, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 196, 'size': 4}
  • id: 109447120
    {'aut_label': '2F', 'centralizer': '8.bb1', 'counter': 7, 'group_counter': 26547, 'group_order': 256, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 1, 'size': 8}
  • id: 109447121
    {'aut_label': '2G', 'centralizer': '8.bs1', 'counter': 8, 'group_counter': 26547, 'group_order': 256, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 12, 'size': 8}
  • id: 109447122
    {'aut_label': '2H', 'centralizer': '8.cd1', 'counter': 9, 'group_counter': 26547, 'group_order': 256, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 3, 'size': 8}
  • id: 109447090
    {'aut_label': '2F', 'centralizer': '8.bb1', 'counter': 10, 'group_counter': 26547, 'group_order': 256, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 97, 'size': 8}
  • id: 109447091
    {'aut_label': '2F', 'centralizer': '8.bb1', 'counter': 11, 'group_counter': 26547, 'group_order': 256, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 73, 'size': 8}
  • id: 109447092
    {'aut_label': '2F', 'centralizer': '8.bb1', 'counter': 12, 'group_counter': 26547, 'group_order': 256, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 41, 'size': 8}
  • id: 109447093
    {'aut_label': '2H', 'centralizer': '8.cd1', 'counter': 13, 'group_counter': 26547, 'group_order': 256, 'label': '2L', 'order': 2, 'powers': [1], 'representative': 35, 'size': 8}
  • id: 109447094
    {'aut_label': '4A', 'centralizer': '2.d1', 'counter': 14, 'group_counter': 26547, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 96, 'size': 2}
  • id: 109447095
    {'aut_label': '4B', 'centralizer': '2.e1', 'counter': 15, 'group_counter': 26547, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 112, 'size': 2}
  • id: 109447096
    {'aut_label': '4C', 'centralizer': '4.q1', 'counter': 16, 'group_counter': 26547, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [3], 'representative': 8, 'size': 4}
  • id: 109447097
    {'aut_label': '4C', 'centralizer': '4.q1', 'counter': 17, 'group_counter': 26547, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [3], 'representative': 136, 'size': 4}
  • id: 109447098
    {'aut_label': '4E', 'centralizer': '4.w1', 'counter': 18, 'group_counter': 26547, 'group_order': 256, 'label': '4E', 'order': 4, 'powers': [2], 'representative': 36, 'size': 4}
  • id: 109447099
    {'aut_label': '4E', 'centralizer': '4.w1', 'counter': 19, 'group_counter': 26547, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [2], 'representative': 100, 'size': 4}
  • id: 109447101
    {'aut_label': '4G', 'centralizer': '4.s1', 'counter': 20, 'group_counter': 26547, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [2], 'representative': 192, 'size': 4}
  • id: 109447102
    {'aut_label': '4H', 'centralizer': '8.d1', 'counter': 21, 'group_counter': 26547, 'group_order': 256, 'label': '4H', 'order': 4, 'powers': [3], 'representative': 40, 'size': 8}
  • id: 109447103
    {'aut_label': '4I', 'centralizer': '8.bi1', 'counter': 22, 'group_counter': 26547, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [3], 'representative': 65, 'size': 8}
  • id: 109447104
    {'aut_label': '4I', 'centralizer': '8.bi1', 'counter': 23, 'group_counter': 26547, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [3], 'representative': 33, 'size': 8}
  • id: 109447105
    {'aut_label': '4I', 'centralizer': '8.bi1', 'counter': 24, 'group_counter': 26547, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [3], 'representative': 9, 'size': 8}
  • id: 109447106
    {'aut_label': '4L', 'centralizer': '8.bu1', 'counter': 25, 'group_counter': 26547, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [2], 'representative': 44, 'size': 8}
  • id: 109447107
    {'aut_label': '4M', 'centralizer': '8.cd1', 'counter': 26, 'group_counter': 26547, 'group_order': 256, 'label': '4M', 'order': 4, 'powers': [2], 'representative': 67, 'size': 8}
  • id: 109447108
    {'aut_label': '4I', 'centralizer': '8.bi1', 'counter': 27, 'group_counter': 26547, 'group_order': 256, 'label': '4N', 'order': 4, 'powers': [3], 'representative': 105, 'size': 8}
  • id: 109447109
    {'aut_label': '4M', 'centralizer': '8.cd1', 'counter': 28, 'group_counter': 26547, 'group_order': 256, 'label': '4O', 'order': 4, 'powers': [2], 'representative': 99, 'size': 8}
  • id: 109447110
    {'aut_label': '4P', 'centralizer': '16.cp1', 'counter': 29, 'group_counter': 26547, 'group_order': 256, 'label': '4P', 'order': 4, 'powers': [5], 'representative': 2, 'size': 16}
  • id: 109447112
    {'aut_label': '4P', 'centralizer': '16.cp1', 'counter': 30, 'group_counter': 26547, 'group_order': 256, 'label': '4Q', 'order': 4, 'powers': [5], 'representative': 34, 'size': 16}
  • id: 109447113
    {'aut_label': '4P', 'centralizer': '16.cp1', 'counter': 31, 'group_counter': 26547, 'group_order': 256, 'label': '4R', 'order': 4, 'powers': [6], 'representative': 10, 'size': 16}
  • id: 109447114
    {'aut_label': '4P', 'centralizer': '16.cp1', 'counter': 32, 'group_counter': 26547, 'group_order': 256, 'label': '4S', 'order': 4, 'powers': [6], 'representative': 42, 'size': 16}
  • id: 109447115
    {'aut_label': '8A', 'centralizer': '16.cd1', 'counter': 33, 'group_counter': 26547, 'group_order': 256, 'label': '8A', 'order': 8, 'powers': [20], 'representative': 11, 'size': 16}
  • id: 109447116
    {'aut_label': '8A', 'centralizer': '16.cd1', 'counter': 34, 'group_counter': 26547, 'group_order': 256, 'label': '8B', 'order': 8, 'powers': [20], 'representative': 43, 'size': 16}
• 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: 4275095
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1a', '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], 'schur_index': 1}
  • id: 4275106
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1b', '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], 'schur_index': 1}
  • id: 4275117
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1c', '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], 'schur_index': 1}
  • id: 4275123
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1d', '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], 'schur_index': 1}
  • id: 4275124
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1e', '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], 'schur_index': 1}
  • id: 4275125
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1f', '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], 'schur_index': 1}
  • id: 4275126
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1g', '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], 'schur_index': 1}
  • id: 4275127
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1h', '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], 'schur_index': 1}
  • id: 4275128
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1i', '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], 'schur_index': 1}
  • id: 4275096
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1j', '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], 'schur_index': 1}
  • id: 4275097
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1k', '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], 'schur_index': 1}
  • id: 4275098
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1l', '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], 'schur_index': 1}
  • id: 4275099
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1m', '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], 'schur_index': 1}
  • id: 4275100
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1n', '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], 'schur_index': 1}
  • id: 4275101
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1o', '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], 'schur_index': 1}
  • id: 4275102
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.1p', '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], 'schur_index': 1}
  • id: 4275103
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -2, 0, 0, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275104
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -2, 0, 0, 2, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275105
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 2, 0, -2, 0, -2, 0, 0, 0, 2, 2, 0, 0, -2, -2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275107
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, -2, -2, 2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275108
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, -2, 0, 0, 0, 0, -2, -2, 0, 2, 2, 0, 0, 2, -2, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275109
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, -2, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275110
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, -2, 2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275111
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275112
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2i', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, 0, -2, 0, 2, 0, 0, 0, -2, -2, 0, 0, 2, -2, -2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275113
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2j', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, 0, 2, 0, -2, 0, 0, 0, -2, -2, 0, 0, 2, -2, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275114
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2k', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, 0, 0, 0, 0, -2, 2, 0, -2, -2, 0, 0, -2, -2, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275115
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.2l', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 2, -2, 0, -2, -2, 0, 0, -2, -2, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275116
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.4a', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275118
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.4b', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275119
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.4c', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275120
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.4d', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275121
    {'cdim': 8, 'counter': 33, 'faithful': True, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.8a', 'multiplicity': 1, 'nt': [16, 529], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4275122
    {'cdim': 8, 'counter': 34, 'faithful': True, 'group': '256.26547', 'group_order': 256, 'image': None, 'label': '256.26547.8b', 'multiplicity': 1, 'nt': [16, 529], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• 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: 6354727
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 256, 'label': '256.26547.1a', '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]]]}
  • id: 6354738
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 128, 'label': '256.26547.1b', '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]]]}
  • id: 6354749
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.26547.1c', '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]]]}
  • id: 6354755
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 128, 'label': '256.26547.1d', '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]]]}
  • id: 6354756
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.26547.1e', '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]]]}
  • id: 6354757
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 128, 'label': '256.26547.1f', '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]]]}
  • id: 6354758
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.26547.1g', '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]]]}
  • id: 6354759
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 128, 'label': '256.26547.1h', '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]]]}
  • id: 6354760
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.26547.1i', '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]]]}
  • id: 6354728
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.26547.1j', '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]]]}
  • id: 6354729
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 128, 'label': '256.26547.1k', '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]]]}
  • id: 6354730
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.26547.1l', '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]]]}
  • id: 6354731
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.26547.1m', '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]]]}
  • id: 6354732
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.26547.1n', '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]]]}
  • id: 6354733
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 128, 'label': '256.26547.1o', '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]]]}
  • id: 6354734
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.26547.1p', '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]]]}
  • id: 6354735
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.n1', 'kernel_order': 32, 'label': '256.26547.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354736
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.m1', 'kernel_order': 32, 'label': '256.26547.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354737
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1', 'kernel_order': 32, 'label': '256.26547.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354739
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1', 'kernel_order': 32, 'label': '256.26547.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354740
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1', 'kernel_order': 32, 'label': '256.26547.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354741
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1', 'kernel_order': 32, 'label': '256.26547.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354742
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1', 'kernel_order': 32, 'label': '256.26547.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354743
    {'center': '4.b1', 'center_index': 4, 'center_order': 64, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1', 'kernel_order': 32, 'label': '256.26547.2h', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354744
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.26547.2i', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354745
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.26547.2j', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354746
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.26547.2k', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354747
    {'center': '4.a1', 'center_index': 4, 'center_order': 64, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.26547.2l', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354748
    {'center': '32.c1', 'center_index': 32, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.c1', 'kernel_order': 4, 'label': '256.26547.4a', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354750
    {'center': '32.c1', 'center_index': 32, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1', 'kernel_order': 4, 'label': '256.26547.4b', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354751
    {'center': '32.c1', 'center_index': 32, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1', 'kernel_order': 4, 'label': '256.26547.4c', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354752
    {'center': '32.c1', 'center_index': 32, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.c1', 'kernel_order': 4, 'label': '256.26547.4d', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6354753
    {'center': '128.a1', 'center_index': 128, 'center_order': 2, 'counter': 33, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '256.26547', 'image_order': 256, 'indicator': 1, 'kernel': '256.a1', 'kernel_order': 1, 'label': '256.26547.8a', 'nt': [16, 529], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]]]}
  • id: 6354754
    {'center': '128.a1', 'center_index': 128, 'center_order': 2, 'counter': 34, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '256.26547', 'group_counter': 26547, 'group_order': 256, 'image': None, 'image_isoclass': '256.26547', 'image_order': 256, 'indicator': 1, 'kernel': '256.a1', 'kernel_order': 1, 'label': '256.26547.8b', 'nt': [16, 529], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]]]}
• 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: 64503851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.26547.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '256.26547', 'subgroup_hash': 26547, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 64503962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.2.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': '128.1759', 'subgroup_hash': 1759, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 64504048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.2.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': '128.854', 'subgroup_hash': 854, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times D_4):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.2.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': '128.2281', 'subgroup_hash': 2281, 'subgroup_order': 128, 'subgroup_tex': 'D_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1750', 'subgroup_hash': 1750, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64504081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.858', 'subgroup_hash': 858, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times C_4^2):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.2.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.213', 'subgroup_hash': 213, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 64503874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64503885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': '64.94', 'subgroup_hash': 94, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.4.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': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.213', 'subgroup_hash': 213, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.256', 'subgroup_hash': 256, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.236', 'subgroup_hash': 236, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64504051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.236', 'subgroup_hash': 236, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.4.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '8.3', '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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': ['U1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '8.3', '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504058
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '8.3', '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': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '8.3', '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: 64504061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '8.3', '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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '8.3', '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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.8.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': '8.3', '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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64504071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.s2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s2', 'outer_equivalence': True, 'perfect': False, '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: 64504077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.u2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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: 64504080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64504083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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: 64504094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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: 64504096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64504115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64504116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64504118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64504123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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: 64504124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.8.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.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': '16.11', '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: 64503855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.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': '16.11', '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: 64503856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.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': '16.11', '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: 64503857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.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': '16.11', '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: 64503858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.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': '16.11', '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.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': ['D', 'Phi', 'L1', 'D1', 'C4'], '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: 64503860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 107, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.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': '16.11', '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: 64503861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 108, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1', '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 109, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.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': '16.11', '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503864
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1', '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.16.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': '16.11', '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503882
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 64503883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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: 64503887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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: 64503892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503895
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503900
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64503902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.ca2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ca2', 'outer_equivalence': True, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503915
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64503919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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: 64503920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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: 64503921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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: 64503922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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: 64503923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64503931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.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: 64503935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64503937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64503939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64503942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64503943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.16.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 64503944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 183, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.32.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': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_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: 64503945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 184, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.32.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': '32.46', '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: 64503946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 185, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': ['U2'], '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: 64503947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 186, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', '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: 64503948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 187, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': ['C5'], '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: 64503949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64503950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64503952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503953
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503954
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64503961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503964
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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: 64503966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64503967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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: 64503969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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: 64503973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64503976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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: 64503977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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: 64503980
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503983
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503984
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503986
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503988
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503995
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 229, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64503997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503998
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64503999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504000
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64504001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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: 64504003
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504004
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64504005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64504009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.32.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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: 64504010
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 242, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26547.64.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': '64.202', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 202, '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': ['L2', 'C6'], '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: 64504011
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 243, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.26547.64.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': '64.138', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 138, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\wr C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504012
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 244, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.26547.64.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': '64.138', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 138, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\wr C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64504014
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504015
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504016
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504017
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504019
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504020
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 251, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504021
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 252, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504022
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 253, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504024
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504025
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.o2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.o2', 'outer_equivalence': True, 'perfect': False, '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: 64504027
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504028
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504030
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504031
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504032
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504033
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504034
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504035
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64504036
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.26547.64.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: 64504037
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 267, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.26547.128.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': '128.1755', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1755, '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': ['Z', 'S', 'U3', 'L3', 'D2', '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: 64504038
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 64504039
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.128.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 64504041
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.128.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: 64504042
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.128.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: 64504043
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.128.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: 64504044
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.26547.128.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: 64504045
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26547', 'ambient_counter': 26547, 'ambient_order': 256, 'ambient_tex': 'D_4^2:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 274, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.26547.256.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': '256.26547', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26547, 'quotient_metabelian': False, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U4', 'L4', 'D3', '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: 64504024
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.b1', '32.bx1', '32.by1', '32.bz1'], 'contains': ['128.b1', '128.d1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7911, -1, 7931, -1], 'generators': [4, 16], 'label': '256.26547.64.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1', 'old_label': '64.n1', 'projective_image': '256.26547', '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: 64503878
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.ba1', '8.bh1', '8.bi1', '8.bn1', '8.bq1', '8.br1'], 'contains': ['32.d1', '32.f1', '32.k1'], 'core': '32.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [7554, -1, 7572, -1], 'generators': [1, 164], 'label': '256.26547.16.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.w1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503879
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.t1', '8.bk1', '8.bm1', '8.bn1', '8.bo1', '8.bp1'], 'contains': ['32.e1', '32.f1', '32.k1'], 'core': '32.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [7437, -1, 7454, -1], 'generators': [1, 208], 'label': '256.26547.16.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.x1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503858
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.e1', 'aut_quo_index': 8, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '32.d1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.f1', '8.g1', '8.x1', '8.y1', '8.be1'], 'contains': ['32.b1', '32.k1'], 'core': '16.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [6165, 1702, 6180, 1684], 'generators': [209, 4], 'label': '256.26547.16.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': ['8.a1', '8.f1', '8.g1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64503851
    {'ambient': '256.26547', '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': '128.a1', 'complements': ['256.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4596, 4890, 4608, 4931], 'generators': [1, 2, 8, 32], 'label': '256.26547.1.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'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '128.1755', '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': '128.1755'}
  • id: 64503852
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 16, 'centralizer': '32.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.d1', '2.e1'], 'contains': ['8.b1', '8.c1', '8.d1', '8.h1', '8.j1', '8.m1', '8.n1', '8.p1', '8.bd1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5358, 9393, 5370, 9472], 'generators': [8, 32, 4, 208], 'label': '256.26547.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.c1', '2.d1', '2.e1'], 'normal_contains': ['8.b1', '8.c1', '8.d1', '8.h1', '8.j1', '8.m1', '8.n1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '128.1755', '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': '32.27'}
  • id: 64503853
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '8.ck1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 32, 'centralizer': '64.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.u1'], 'contains': ['16.ch1', '16.cj1', '16.co1', '16.cp1'], 'core': '64.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [649, -1, 650, -1], 'generators': [195, 218, 240], 'label': '256.26547.8.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '8.ck1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ck1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64503854
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '32.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.b1', '8.o1', '8.p1', '8.q1', '8.r1'], 'contains': ['32.a1', '32.b1', '32.d1', '32.m1'], 'core': '16.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5043, 3070, 5055, 3095], 'generators': [32, 4, 16], 'label': '256.26547.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['32.a1', '32.b1', '32.d1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64503855
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '16.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.c1', '8.d1', '8.t1', '8.v1', '8.w1'], 'contains': ['32.a1', '32.c1', '32.e1', '32.q1', '32.r1'], 'core': '16.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5196, 6231, 5208, 6273], 'generators': [32, 208, 16], 'label': '256.26547.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.b1', '8.c1', '8.d1'], 'normal_contains': ['32.a1', '32.c1', '32.e1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64503856
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.c1', 'aut_quo_index': 8, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.c1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.e1', '8.g1', '8.z1', '8.bb1', '8.bc1'], 'contains': ['32.b1', '32.f1', '32.t1', '32.by1'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [5607, 2401, 5620, 2390], 'generators': [1, 4, 16, 128], 'label': '256.26547.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.a1', '8.e1', '8.g1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '128.1755', 'quotient_action_image': '16.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64503857
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '16.d1', 'aut_quo_index': 16, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.e1', '8.f1', '8.ba1', '8.bd1', '8.bf1', '8.bg1'], 'contains': ['32.b1', '32.c1', '32.d1', '32.w1', '32.x1'], 'core': '16.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [4889, 3843, 4901, 3875], 'generators': [240, 4, 16], 'label': '256.26547.16.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': ['8.b1', '8.e1', '8.f1'], 'normal_contains': ['32.b1', '32.c1', '32.d1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': '128.1755', 'quotient_action_image': '16.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64503900
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '8.o1', '8.bh1', '8.bi1', '8.bn1'], 'contains': ['32.d1', '32.k1'], 'core': '32.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [6574, -1, 6589, -1], 'generators': [209, 116], 'label': '256.26547.16.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bq1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503859
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.f1', 'aut_quo_index': 2520, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '32.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.g1', '8.h1', '8.i1', '8.j1', '8.k1', '8.l1'], 'contains': ['32.b1', '32.e1', '32.ba1'], 'core': '16.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [4593, 4737, 4604, 4766], 'generators': [4, 208, 16], 'label': '256.26547.16.f1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.f1', 'normal_contained_in': ['8.b1', '8.g1', '8.h1', '8.i1', '8.j1', '8.k1', '8.l1'], 'normal_contains': ['32.b1', '32.e1'], 'normalizer': '1.a1', 'old_label': '16.f1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64503860
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.g1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '32.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.h1', '8.m1', '8.bk1', '8.bv1'], 'contains': ['32.e1', '32.g1', '32.bi1'], 'core': '16.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [5492, 8746, 5505, 8862], 'generators': [28, 208, 16], 'label': '256.26547.16.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': ['8.c1', '8.h1', '8.m1'], 'normal_contains': ['32.e1'], 'normalizer': '1.a1', 'old_label': '16.g1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64503861
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '16.h1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '8.h1', '8.n1', '8.bm1', '8.bw1'], 'contains': ['32.e1', '32.i1'], 'core': '16.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [5692, 7583, 5705, 7636], 'generators': [8, 208], 'label': '256.26547.16.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': ['8.d1', '8.h1', '8.n1'], 'normal_contains': ['32.e1'], 'normalizer': '1.a1', 'old_label': '16.h1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64503862
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '32.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.m1', '8.n1', '8.bn1', '8.bz1', '8.cb1'], 'contains': ['32.d1', '32.e1', '32.br1'], 'core': '16.i1', 'coset_action_label': None, 'count': 1, 'diagramx': [4737, 5458, 4747, 5493], 'generators': [164, 208, 16], 'label': '256.26547.16.i1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': ['8.b1', '8.m1', '8.n1'], 'normal_contains': ['32.d1', '32.e1'], 'normalizer': '1.a1', 'old_label': '16.i1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64503863
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 8, 'centralizer': '64.b1', 'complements': ['64.x1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.b1', '8.i1', '8.q1', '8.v1', '8.bf1', '8.bz1', '8.cc1', '8.cd1', '8.ce1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2776, 1297, 2782, 1308], 'generators': [3, 32, 4, 16, 208], 'label': '256.26547.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.b1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '128.1755', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 64503864
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '16.j1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '8.j1', '8.m1', '8.bo1', '8.bx1'], 'contains': ['32.e1', '32.j1'], 'core': '16.j1', 'coset_action_label': None, 'count': 1, 'diagramx': [5777, 8073, 5791, 8183], 'generators': [40, 208], 'label': '256.26547.16.j1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': ['8.d1', '8.j1', '8.m1'], 'normal_contains': ['32.e1'], 'normalizer': '1.a1', 'old_label': '16.j1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64503865
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.k1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '32.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.j1', '8.n1', '8.bp1', '8.by1'], 'contains': ['32.e1', '32.l1', '32.bs1'], 'core': '16.k1', 'coset_action_label': None, 'count': 1, 'diagramx': [5349, 7005, 5362, 7053], 'generators': [188, 208, 16], 'label': '256.26547.16.k1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': ['8.c1', '8.j1', '8.n1'], 'normal_contains': ['32.e1'], 'normalizer': '1.a1', 'old_label': '16.k1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64503866
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.o1', '8.s1', '8.s2', '8.t1', '8.u1', '8.u2'], 'contains': ['32.a1', '32.f1', '32.k1', '32.bv1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8272, -1, 8291, -1], 'generators': [1, 32, 128], 'label': '256.26547.16.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.l1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64503867
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.p1', '8.s1', '8.s2'], 'contains': ['32.a1', '32.g1', '32.l1', '32.n1'], 'core': '32.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6928, -1, 6944, -1], 'generators': [28, 32, 16], 'label': '256.26547.16.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.m1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64503868
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1', '8.v1'], 'contains': ['32.a1', '32.h1', '32.o1', '32.p1', '32.s1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2721, -1, 2728, -1], 'generators': [3, 32, 16], 'label': '256.26547.16.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.n1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64503869
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '8.p1', '8.u1', '8.u2'], 'contains': ['32.a1', '32.i1', '32.j1', '32.bw1'], 'core': '32.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9523, -1, 9545, -1], 'generators': [8, 32, 128], 'label': '256.26547.16.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.o1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503870
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.o1', '8.x1', '8.y1', '8.ba1', '8.bb1', '8.bc1'], 'contains': ['32.b1', '32.f1', '32.k1', '32.bx1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [8042, -1, 8061, -1], 'generators': [1, 212, 128], 'label': '256.26547.16.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.p1', 'projective_image': '128.1755', '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: 64503871
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.h1', '8.p1', '8.x1', '8.bb1', '8.bd1'], 'contains': ['32.b1', '32.g1', '32.i1', '32.bz1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7189, -1, 7206, -1], 'generators': [8, 4, 128], 'label': '256.26547.16.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.q1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503872
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.w1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.i1', '8.q1', '8.z1', '8.be1', '8.bf1'], 'contains': ['32.b1', '32.h1', '32.u1', '32.v1', '32.y1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1215, -1, 1219, -1], 'generators': [3, 4, 16], 'label': '256.26547.16.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.r1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64503873
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.j1', '8.p1', '8.y1', '8.bc1', '8.bd1'], 'contains': ['32.b1', '32.j1', '32.l1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7058, -1, 7075, -1], 'generators': [40, 4], 'label': '256.26547.16.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.s1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503874
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 16, 'centralizer': '64.c1', 'complements': ['64.x1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.e1'], 'contains': ['8.b1', '8.k1', '8.r1', '8.bg1'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3126, 2875, 3132, 2899], 'generators': [218, 32, 208], 'label': '256.26547.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.b1', '2.e1'], 'normal_contains': ['8.b1', '8.k1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '128.1755', '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': '64.138'}
  • id: 64503875
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.x1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.k1', '8.r1', '8.z1', '8.be1', '8.bg1'], 'contains': ['32.b1', '32.z1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1086, -1, 1088, -1], 'generators': [218, 16], 'label': '256.26547.16.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.t1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64503876
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.s1', '8.x1', '8.bb1', '8.bh1', '8.bj1', '8.bk1', '8.bq1'], 'contains': ['32.f1', '32.g1', '32.k1', '32.ca1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8618, -1, 8639, -1], 'generators': [5, 28, 128], 'label': '256.26547.16.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.u1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503877
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.v1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.u1', '8.x1', '8.bb1', '8.bi1', '8.bl1', '8.bm1', '8.br1'], 'contains': ['32.f1', '32.i1', '32.k1', '32.cb1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9001, -1, 9022, -1], 'generators': [1, 8, 128], 'label': '256.26547.16.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.v1', 'projective_image': '128.1755', '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: 64503880
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.u2', '8.y1', '8.bc1', '8.bh1', '8.bl1', '8.bo1', '8.bq1'], 'contains': ['32.f1', '32.j1', '32.k1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9382, -1, 9404, -1], 'generators': [5, 40], 'label': '256.26547.16.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.y1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503881
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.s2', '8.y1', '8.bc1', '8.bi1', '8.bj1', '8.bp1', '8.br1'], 'contains': ['32.f1', '32.k1', '32.l1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7912, -1, 7931, -1], 'generators': [1, 188], 'label': '256.26547.16.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.z1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503882
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.s2', '8.bb1', '8.bk1', '8.bq1', '8.bs1'], 'contains': ['32.f1', '32.g1', '32.bb1', '32.cc1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8157, -1, 8176, -1], 'generators': [1, 28, 16, 128], 'label': '256.26547.16.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.ba1', 'projective_image': '128.1755', '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: 64503883
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.t1', '8.ba1', '8.bj1', '8.bl1', '8.bs1', '8.bt1'], 'contains': ['32.c1', '32.f1', '32.bc1', '32.bd1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [6689, -1, 6704, -1], 'generators': [1, 240, 16], 'label': '256.26547.16.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bb1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503884
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.u2', '8.bb1', '8.bm1', '8.br1', '8.bt1'], 'contains': ['32.f1', '32.i1', '32.cd1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9154, -1, 9176, -1], 'generators': [5, 8, 128], 'label': '256.26547.16.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bc1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503885
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 8, 'centralizer': '64.b1', 'complements': ['64.x1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.b1', '8.l1', '8.w1', '8.cb1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [4475, 2001, 4485, 2019], 'generators': [219, 32, 4], 'label': '256.26547.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.b1', '8.l1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '128.1755', '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': '64.138'}
  • id: 64503886
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.o1', '8.bn1', '8.bq1', '8.br1'], 'contains': ['32.d1', '32.f1', '32.be1'], 'core': '32.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [6459, -1, 6474, -1], 'generators': [1, 116, 16], 'label': '256.26547.16.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bd1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503887
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.u1', '8.bc1', '8.bo1', '8.bq1', '8.bt1'], 'contains': ['32.f1', '32.j1', '32.ce1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9676, -1, 9698, -1], 'generators': [1, 40, 128], 'label': '256.26547.16.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.be1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503888
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '32.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.s1', '8.bc1', '8.bp1', '8.br1', '8.bs1'], 'contains': ['32.f1', '32.l1', '32.bf1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7782, -1, 7800, -1], 'generators': [5, 188, 16], 'label': '256.26547.16.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bf1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503889
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.bd1', '8.bj1', '8.bs1', '8.bu1'], 'contains': ['32.c1', '32.g1', '32.l1', '32.bg1', '32.bh1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6306, -1, 6321, -1], 'generators': [28, 240, 16], 'label': '256.26547.16.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bg1', 'projective_image': '128.1755', '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: 64503890
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.m1', '8.p1', '8.bd1', '8.bh1', '8.bq1'], 'contains': ['32.d1', '32.g1', '32.j1'], 'core': '32.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [7319, -1, 7336, -1], 'generators': [28, 164], 'label': '256.26547.16.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bh1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503891
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '32.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.s2', '8.x1', '8.bh1', '8.bk1', '8.bu1'], 'contains': ['32.g1', '32.k1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8489, -1, 8508, -1], 'generators': [209, 28], 'label': '256.26547.16.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bi1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503892
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1', '8.bf1'], 'contains': ['32.c1', '32.h1', '32.bj1', '32.bm1', '32.bp1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2343, -1, 2348, -1], 'generators': [3, 240, 16], 'label': '256.26547.16.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bj1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503893
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.q1', '8.bf1', '8.bz1'], 'contains': ['32.d1', '32.h1', '32.bk1', '32.bn1', '32.bq1'], 'core': '32.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [1767, -1, 1771, -1], 'generators': [3, 164, 16], 'label': '256.26547.16.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bk1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503894
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.i1', '8.v1', '8.bv1', '8.bw1', '8.bx1', '8.by1', '8.bz1'], 'contains': ['32.e1', '32.h1', '32.bl1', '32.bo1', '32.bt1'], 'core': '32.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [3559, -1, 3567, -1], 'generators': [3, 208, 16], 'label': '256.26547.16.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '16.bl1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64503895
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '8.bd1', '8.bl1', '8.bt1', '8.ca1'], 'contains': ['32.c1', '32.i1', '32.j1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8876, -1, 8897, -1], 'generators': [8, 240], 'label': '256.26547.16.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bm1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503896
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '128.a1', 'complements': ['64.x1'], 'conjugacy_class_count': 8, 'contained_in': ['2.a1', '2.f1', '2.g1'], 'contains': ['8.g1', '8.i1', '8.k1', '8.z1', '8.be1'], 'core': '4.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [3308, 4295, 3316, 4331], 'generators': [3, 218, 208], 'label': '256.26547.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.a1', '2.f1', '2.g1'], 'normal_contains': ['8.g1', '8.i1', '8.k1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '128.1755', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 64503897
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '8.t1', '8.ba1', '8.bj1', '8.bl1', '8.bu1', '8.ca1'], 'contains': ['32.c1', '32.k1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [7661, -1, 7680, -1], 'generators': [209, 240], 'label': '256.26547.16.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bn1', 'projective_image': '128.1755', '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: 64503898
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.n1', '8.p1', '8.bd1', '8.bi1', '8.br1'], 'contains': ['32.d1', '32.i1', '32.l1'], 'core': '32.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [6809, -1, 6824, -1], 'generators': [8, 164], 'label': '256.26547.16.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bo1', 'projective_image': '128.1755', '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: 64503899
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.bp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.u2', '8.x1', '8.bi1', '8.bm1', '8.ca1'], 'contains': ['32.i1', '32.k1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9275, -1, 9296, -1], 'generators': [213, 8], 'label': '256.26547.16.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bp1', 'projective_image': '128.1755', '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: 64503901
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.l1', '8.w1', '8.bv1', '8.bw1', '8.bx1', '8.by1', '8.cb1'], 'contains': ['32.e1', '32.bu1'], 'core': '32.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [4374, -1, 4384, -1], 'generators': [219, 16], 'label': '256.26547.16.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '16.br1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64503902
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.u1', '8.y1', '8.bh1', '8.bo1', '8.ca1'], 'contains': ['32.j1', '32.k1', '32.cf1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9818, -1, 9841, -1], 'generators': [209, 40, 128], 'label': '256.26547.16.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bs1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503903
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '16.bt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.s1', '8.y1', '8.bi1', '8.bp1', '8.bu1'], 'contains': ['32.k1', '32.l1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8387, -1, 8406, -1], 'generators': [213, 188], 'label': '256.26547.16.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.bt1', 'projective_image': '128.1755', '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: 64503904
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.bj1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.q1', '8.cc1', '8.cd1'], 'contains': ['32.m1', '32.o1', '32.s1', '32.u1', '32.y1', '32.bk1', '32.bq1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1671, -1, 1675, -1], 'generators': [19, 32, 4], 'label': '256.26547.16.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bu1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503905
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.bj1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.q1', '8.cd1', '8.ce1'], 'contains': ['32.m1', '32.o1', '32.p1', '32.u1', '32.v1', '32.bk1', '32.bn1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1552, -1, 1555, -1], 'generators': [3, 32, 4], 'label': '256.26547.16.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bv1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503906
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.cd1'], 'contains': ['32.m1', '32.q1', '32.w1', '32.ba1', '32.br1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3463, -1, 3471, -1], 'generators': [48, 4, 208], 'label': '256.26547.16.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bw1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503907
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '128.a1', 'complements': ['64.t1', '64.x1'], 'conjugacy_class_count': 8, 'contained_in': ['2.b1', '2.f1', '2.g1'], 'contains': ['8.g1', '8.k1', '8.l1'], 'core': '4.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [4636, 5647, 4646, 5695], 'generators': [1, 218], 'label': '256.26547.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.b1', '2.f1', '2.g1'], 'normal_contains': ['8.g1', '8.k1', '8.l1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '128.1755', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '128.1755'}
  • id: 64503908
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.cc1', '8.ce1'], 'contains': ['32.m1', '32.r1', '32.x1', '32.ba1', '32.br1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2984, -1, 2991, -1], 'generators': [32, 4, 208], 'label': '256.26547.16.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.bx1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503909
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.by1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.cf1'], 'contains': ['32.n1', '32.q1', '32.bg1', '32.bi1', '32.bs1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4474, -1, 4484, -1], 'generators': [28, 48, 208], 'label': '256.26547.16.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '16.by1', 'projective_image': '128.1755', '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': '8.3'}
  • id: 64503910
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.bz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.cg1', '8.ch1'], 'contains': ['32.n1', '32.r1', '32.bh1', '32.bi1', '32.bs1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [4274, -1, 4284, -1], 'generators': [28, 32, 208], 'label': '256.26547.16.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '16.bz1', 'projective_image': '128.1755', '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': '8.3'}
  • id: 64503911
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.ca1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.ca1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1', '8.cd1'], 'contains': ['32.p1', '32.q1', '32.s1', '32.bj1', '32.bl1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2569, -1, 2575, -1], 'generators': [7, 48, 208], 'label': '256.26547.16.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.ca1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503912
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.ca2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.ca2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.v1', '8.cd1', '8.cf1'], 'contains': ['32.o1', '32.q1', '32.bj1', '32.bo1', '32.bt1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3080, -1, 3088, -1], 'generators': [3, 48, 208], 'label': '256.26547.16.ca2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '16.ca2', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ca2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64503913
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.cb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1', '8.cc1', '8.ce1'], 'contains': ['32.o1', '32.r1', '32.bl1', '32.bm1', '32.bp1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2439, -1, 2444, -1], 'generators': [7, 32, 208], 'label': '256.26547.16.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.cb1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503914
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.cc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1', '8.ce1', '8.cg1'], 'contains': ['32.p1', '32.r1', '32.bm1', '32.bo1'], 'core': '64.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [2865, -1, 2871, -1], 'generators': [3, 32, 208], 'label': '256.26547.16.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '16.cc1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64503915
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.cd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.cd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1', '8.cf1'], 'contains': ['32.q1', '32.bu1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4155, -1, 4165, -1], 'generators': [79, 48], 'label': '256.26547.16.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '16.cd1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503916
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.ce1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1', '8.cc1', '8.ch1'], 'contains': ['32.r1', '32.s1', '32.bp1', '32.bt1'], 'core': '64.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [3200, -1, 3208, -1], 'generators': [19, 32, 208], 'label': '256.26547.16.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '16.ce1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64503917
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1', '8.cg1', '8.ch1'], 'contains': ['32.r1', '32.bu1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [3836, -1, 3845, -1], 'generators': [79, 32], 'label': '256.26547.16.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '16.cf1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503918
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 8, 'centralizer': '64.a1', 'complements': ['64.t1'], 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '2.f1'], 'contains': ['8.g1', '8.h1', '8.x1', '8.bb1', '8.bk1', '8.bm1'], 'core': '4.h1', 'coset_action_label': None, 'count': 2, 'diagramx': [7613, 8110, 7630, 8178], 'generators': [1, 8, 4, 208], 'label': '256.26547.4.h1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1', 'normal_contained_in': ['2.c1', '2.f1'], 'normal_contains': ['8.g1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '128.1755', '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': '64.202'}
  • id: 64503919
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.z1', '8.ci1', '8.cj1'], 'contains': ['32.t1', '32.v1', '32.z1', '32.cg1'], 'core': '128.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [62, -1, 62, -1], 'generators': [211, 218, 128], 'label': '256.26547.16.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '16.cg1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503920
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '16.ch1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.z1', '8.ci1', '8.ck1'], 'contains': ['32.t1', '32.y1', '32.z1'], 'core': '128.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [279, -1, 279, -1], 'generators': [195, 218], 'label': '256.26547.16.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '16.ch1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64503921
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '16.ci1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.ci1'], 'contains': ['32.t1', '32.w1', '32.bc1', '32.be1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3343, -1, 3351, -1], 'generators': [1, 224, 4], 'label': '256.26547.16.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '16.ci1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503922
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '16.cj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.cj1', '8.ck1'], 'contains': ['32.t1', '32.x1', '32.bd1', '32.be1'], 'core': '64.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [956, -1, 957, -1], 'generators': [1, 240, 4], 'label': '256.26547.16.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '16.cj1', 'projective_image': '128.1755', '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': '8.5'}
  • id: 64503923
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.ck1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bf1', '8.cd1'], 'contains': ['32.u1', '32.w1', '32.bj1', '32.bn1', '32.bq1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1431, -1, 1435, -1], 'generators': [211, 224, 4], 'label': '256.26547.16.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.ck1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503924
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.ck2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.bf1', '8.cd1', '8.ci1'], 'contains': ['32.v1', '32.w1', '32.y1', '32.bj1', '32.bk1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [802, -1, 804, -1], 'generators': [3, 224, 4], 'label': '256.26547.16.ck2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.ck2', 'projective_image': '128.1755', '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': '8.3'}
  • id: 64503925
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bf1', '8.cc1', '8.ce1'], 'contains': ['32.u1', '32.x1', '32.bk1', '32.bm1', '32.bp1'], 'core': '64.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [1335, -1, 1339, -1], 'generators': [211, 240, 4], 'label': '256.26547.16.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.cl1', 'projective_image': '128.1755', '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: 64503926
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bf1', '8.ce1', '8.cj1'], 'contains': ['32.v1', '32.x1', '32.bm1', '32.bn1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [506, -1, 507, -1], 'generators': [3, 240, 4], 'label': '256.26547.16.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.cm1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64503927
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bg1', '8.ci1'], 'contains': ['32.w1', '32.z1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [386, -1, 387, -1], 'generators': [218, 224], 'label': '256.26547.16.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '16.cn1', 'projective_image': '128.1755', '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: 64503928
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.co1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bf1', '8.cc1', '8.ck1'], 'contains': ['32.x1', '32.y1', '32.bp1', '32.bq1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [649, -1, 650, -1], 'generators': [19, 240, 4], 'label': '256.26547.16.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.co1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64503929
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 8, 'centralizer': '64.a1', 'complements': ['64.t1'], 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '2.g1'], 'contains': ['8.g1', '8.j1', '8.y1', '8.bc1', '8.bo1', '8.bp1'], 'core': '4.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [7463, 6589, 7479, 6645], 'generators': [1, 40, 4, 208], 'label': '256.26547.4.i1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1', 'normal_contained_in': ['2.c1', '2.g1'], 'normal_contains': ['8.g1', '8.j1'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': '128.1755', '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': '64.202'}
  • id: 64503930
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.cp1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bg1', '8.cj1', '8.ck1'], 'contains': ['32.x1', '32.z1'], 'core': '64.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [177, -1, 177, -1], 'generators': [218, 240], 'label': '256.26547.16.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '16.cp1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503931
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.i1', '8.cc1', '8.cd1'], 'contains': ['32.u1', '32.y1', '32.ba1', '32.bl1', '32.bt1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2007, -1, 2012, -1], 'generators': [19, 4, 208], 'label': '256.26547.16.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.cq1', 'projective_image': '128.1755', '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: 64503932
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cr1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.i1', '8.cd1', '8.ce1'], 'contains': ['32.u1', '32.v1', '32.ba1', '32.bl1', '32.bo1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1887, -1, 1891, -1], 'generators': [3, 4, 208], 'label': '256.26547.16.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.cr1', 'projective_image': '128.1755', '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: 64503933
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '16.cs1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bs1'], 'contains': ['32.bb1', '32.bc1', '32.bf1', '32.bg1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [6035, -1, 6049, -1], 'generators': [5, 204, 224], 'label': '256.26547.16.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bs1', 'old_label': '16.cs1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503934
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '16.ct1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bs1'], 'contains': ['32.bb1', '32.bd1', '32.bf1', '32.bh1'], 'core': '64.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [5893, -1, 5906, -1], 'generators': [1, 28, 240], 'label': '256.26547.16.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bs1', 'old_label': '16.ct1', 'projective_image': '128.1755', '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: 64503935
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bv1', '8.cf1', '8.cg1'], 'contains': ['32.bi1', '32.bo1', '32.bu1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3747, -1, 3755, -1], 'generators': [3, 28], 'label': '256.26547.16.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '16.cu1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cu1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64503936
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cv1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bv1', '8.cf1', '8.ch1'], 'contains': ['32.bi1', '32.bt1', '32.bu1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4033, -1, 4042, -1], 'generators': [19, 28], 'label': '256.26547.16.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '16.cv1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cv1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64503937
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cw1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bz1', '8.cc1', '8.cd1'], 'contains': ['32.bk1', '32.bl1', '32.bq1', '32.br1', '32.bt1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2222, -1, 2228, -1], 'generators': [19, 164, 208], 'label': '256.26547.16.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.cw1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64503938
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cx1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.by1', '8.cf1', '8.cg1'], 'contains': ['32.bo1', '32.bs1', '32.bu1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3658, -1, 3666, -1], 'generators': [3, 188], 'label': '256.26547.16.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '16.cx1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cx1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64503939
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cy1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.bz1', '8.cd1', '8.ce1'], 'contains': ['32.bk1', '32.bl1', '32.bn1', '32.bo1', '32.br1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2102, -1, 2108, -1], 'generators': [3, 164, 208], 'label': '256.26547.16.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.cy1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cy1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64503940
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.j1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '2.f1'], 'contains': ['8.h1', '8.i1', '8.l1', '8.bv1', '8.bw1'], 'core': '4.j1', 'coset_action_label': None, 'count': 2, 'diagramx': [4346, 5001, 4356, 5042], 'generators': [3, 8, 4], 'label': '256.26547.4.j1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1', 'normal_contained_in': ['2.d1', '2.f1'], 'normal_contains': ['8.h1', '8.i1', '8.l1'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 64503941
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '16.cz1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.by1', '8.cf1', '8.ch1'], 'contains': ['32.bs1', '32.bt1', '32.bu1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3935, -1, 3944, -1], 'generators': [19, 188], 'label': '256.26547.16.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '16.cz1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cz1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64503942
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '16.da1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.u1'], 'contains': ['32.bv1', '32.bw1', '32.cb1', '32.ce1', '32.cf1'], 'core': '256.a1', 'coset_action_label': '16T529', 'count': 32, 'diagramx': [9938, -1, 9962, -1], 'generators': [1, 8, 32], 'label': '256.26547.16.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1', 'old_label': '16.da1', 'projective_image': '256.26547', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.da1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64503943
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '16.db1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.f1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.bb1'], 'contains': ['32.bx1', '32.by1', '32.bz1', '32.ca1', '32.cb1', '32.cc1', '32.cd1'], 'core': '256.a1', 'coset_action_label': '16T653', 'count': 64, 'diagramx': [8761, -1, 8782, -1], 'generators': [1, 8, 4], 'label': '256.26547.16.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1', 'old_label': '16.db1', 'projective_image': '256.26547', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.db1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64503944
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '32.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.l1', '16.m1', '16.n1', '16.o1'], 'contains': ['64.a1', '64.d1', '64.m1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6012, 4416, 6026, 4454], 'generators': [32, 16, 128], 'label': '256.26547.32.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64503945
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '32.b1', 'aut_quo_index': 192, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.e1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.c1', '16.d1', '16.e1', '16.f1', '16.p1', '16.q1', '16.r1', '16.s1', '16.t1'], 'contains': ['64.a1', '64.e1', '64.n1'], 'core': '32.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5568, 3169, 5581, 3196], 'generators': [4, 16, 128], 'label': '256.26547.32.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.c1', '16.d1', '16.e1', '16.f1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64503946
    {'ambient': '256.26547', 'aut_centralizer_order': 1024, 'aut_label': '32.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.d1', '16.bb1', '16.bg1', '16.bj1', '16.bm1', '16.bn1'], 'contains': ['64.a1', '64.b1', '64.c1'], 'core': '32.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5824, 4990, 5837, 5032], 'generators': [240, 16], 'label': '256.26547.32.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': ['16.b1', '16.d1'], 'normal_contains': ['64.a1', '64.b1', '64.c1'], 'normalizer': '1.a1', 'old_label': '32.c1', 'projective_image': '128.1755', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64503947
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '32.d1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.f1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.d1', '16.i1', '16.w1', '16.bd1', '16.bh1', '16.bk1', '16.bo1', '16.bq1'], 'contains': ['64.a1', '64.i1'], 'core': '32.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [5681, 3843, 5695, 3875], 'generators': [164, 16], 'label': '256.26547.32.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': ['16.a1', '16.d1', '16.i1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.d1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64503948
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '32.e1', 'aut_quo_index': 96, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.f1', '16.g1', '16.h1', '16.i1', '16.j1', '16.k1', '16.x1', '16.bl1', '16.br1'], 'contains': ['64.a1', '64.j1'], 'core': '32.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5021, 6615, 5033, 6661], 'generators': [208, 16], 'label': '256.26547.32.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': ['16.b1', '16.f1', '16.g1', '16.h1', '16.i1', '16.j1', '16.k1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.e1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64503949
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '16.l1', '16.p1', '16.u1', '16.v1', '16.w1', '16.x1', '16.y1', '16.z1', '16.ba1', '16.bb1', '16.bc1', '16.bd1', '16.be1', '16.bf1'], 'contains': ['64.a1', '64.f1', '64.o1', '64.o2'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7956, -1, 7975, -1], 'generators': [1, 16, 128], 'label': '256.26547.32.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.f1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64503950
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '16.m1', '16.q1', '16.u1', '16.ba1', '16.bg1', '16.bh1', '16.bi1'], 'contains': ['64.a1', '64.g1', '64.p1'], 'core': '64.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7189, -1, 7206, -1], 'generators': [28, 16, 128], 'label': '256.26547.32.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.g1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64503951
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.k1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 16, 'centralizer': '64.c1', 'complements': ['64.t1'], 'conjugacy_class_count': 2, 'contained_in': ['2.e1', '2.f1'], 'contains': ['8.h1', '8.k1'], 'core': '4.k1', 'coset_action_label': None, 'count': 2, 'diagramx': [4925, 8624, 4937, 8698], 'generators': [2, 8], 'label': '256.26547.4.k1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1', 'normal_contained_in': ['2.e1', '2.f1'], 'normal_contains': ['8.h1', '8.k1'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': '128.1755', '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': '64.138'}
  • id: 64503952
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.n1', '16.r1', '16.bj1', '16.bk1', '16.bl1'], 'contains': ['64.a1', '64.h1', '64.l1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2500, -1, 2506, -1], 'generators': [3, 16], 'label': '256.26547.32.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.h1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64503953
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1', '16.o1', '16.q1', '16.v1', '16.bc1', '16.bm1', '16.bo1', '16.bp1'], 'contains': ['64.a1', '64.q1'], 'core': '64.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8523, -1, 8543, -1], 'generators': [8, 128], 'label': '256.26547.32.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.i1', 'projective_image': '128.1755', '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: 64503954
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1', '16.o1', '16.s1', '16.y1', '16.be1', '16.bh1', '16.bm1', '16.bs1'], 'contains': ['64.a1', '64.r1'], 'core': '64.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8740, -1, 8760, -1], 'generators': [40, 128], 'label': '256.26547.32.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.j1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503955
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bi1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.e1', '16.l1', '16.p1', '16.u1', '16.v1', '16.w1', '16.x1', '16.y1', '16.z1', '16.bi1', '16.bn1', '16.bp1', '16.bq1', '16.bs1', '16.bt1'], 'contains': ['64.a1', '64.s1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8145, -1, 8165, -1], 'generators': [209, 128], 'label': '256.26547.32.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.k1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503956
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.bu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1', '16.m1', '16.s1', '16.z1', '16.bf1', '16.bg1', '16.bo1', '16.bt1'], 'contains': ['64.a1', '64.k1'], 'core': '64.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6867, -1, 6884, -1], 'generators': [188, 16], 'label': '256.26547.32.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.l1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503957
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.bu1', '16.bv1', '16.bw1', '16.bx1'], 'contains': ['64.d1', '64.e1', '64.i1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2944, -1, 2951, -1], 'generators': [32, 4], 'label': '256.26547.32.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.m1', 'projective_image': '128.1755', '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: 64503958
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1', '16.by1', '16.bz1'], 'contains': ['64.d1', '64.g1', '64.k1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4713, -1, 4685, -1], 'generators': [28, 32], 'label': '256.26547.32.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '32.n1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503959
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.ca2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.n1', '16.bu1', '16.bv1', '16.ca2', '16.cb1'], 'contains': ['64.d1', '64.h1', '64.l1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2283, -1, 2288, -1], 'generators': [7, 32], 'label': '256.26547.32.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.o1', 'projective_image': '128.1755', '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: 64503960
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.ca1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1', '16.bv1', '16.ca1', '16.cc1'], 'contains': ['64.d1', '64.h1', '64.t1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2721, -1, 2728, -1], 'generators': [3, 32, 128], 'label': '256.26547.32.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.p1', 'projective_image': '128.1755', '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: 64503961
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.bw1', '16.by1', '16.ca1', '16.ca2', '16.cd1'], 'contains': ['64.b1', '64.d1', '64.j1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3569, -1, 3577, -1], 'generators': [48, 208], 'label': '256.26547.32.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '32.q1', 'projective_image': '128.1755', '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: 64503962
    {'ambient': '256.26547', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1024.dlr', 'aut_weyl_index': 4, 'centralizer': '128.a1', 'complements': ['128.f1', '128.e1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.d1', '4.f1', '4.n1', '4.u1', '4.w1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2951, 2012, 2958, 2029], 'generators': [3, 218, 32, 208], 'label': '256.26547.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.d1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '128.1755', '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': '128.1755'}
  • id: 64503963
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.l1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': ['64.x1'], 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '2.g1'], 'contains': ['8.i1', '8.j1', '8.l1', '8.bx1', '8.by1'], 'core': '4.l1', 'coset_action_label': None, 'count': 2, 'diagramx': [4249, 3590, 4259, 3621], 'generators': [3, 40, 4], 'label': '256.26547.4.l1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1', 'normal_contained_in': ['2.d1', '2.g1'], 'normal_contains': ['8.i1', '8.j1', '8.l1'], 'normalizer': '1.a1', 'old_label': '4.l1', 'projective_image': '128.1755', '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': '64.138'}
  • id: 64503964
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.bx1', '16.bz1', '16.cb1', '16.cc1', '16.ce1', '16.cf1'], 'contains': ['64.c1', '64.d1', '64.j1'], 'core': '64.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [3353, -1, 3360, -1], 'generators': [32, 208], 'label': '256.26547.32.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '32.r1', 'projective_image': '128.1755', '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: 64503965
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.ca1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1', '16.bu1', '16.ca1', '16.ce1'], 'contains': ['64.d1', '64.l1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2836, -1, 2842, -1], 'generators': [19, 32], 'label': '256.26547.32.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.s1', 'projective_image': '128.1755', '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: 64503966
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '16.cg1', '16.ch1', '16.ci1', '16.cj1'], 'contains': ['64.e1', '64.f1', '64.u1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1261, -1, 1264, -1], 'generators': [1, 4, 128], 'label': '256.26547.32.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '32.t1', 'projective_image': '128.1755', '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: 64503967
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.ck1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.r1', '16.bu1', '16.bv1', '16.ck1', '16.cl1', '16.cq1', '16.cr1'], 'contains': ['64.e1', '64.h1', '64.l1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1624, -1, 1628, -1], 'generators': [211, 4], 'label': '256.26547.32.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.u1', 'projective_image': '128.1755', '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: 64503968
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.r1', '16.bv1', '16.cg1', '16.ck2', '16.cm1', '16.cr1'], 'contains': ['64.e1', '64.h1', '64.v1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1175, -1, 1178, -1], 'generators': [3, 4, 128], 'label': '256.26547.32.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.v1', 'projective_image': '128.1755', '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': '8.3'}
  • id: 64503969
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.bw1', '16.ci1', '16.ck1', '16.ck2', '16.cn1'], 'contains': ['64.b1', '64.e1', '64.i1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2391, -1, 2397, -1], 'generators': [224, 4], 'label': '256.26547.32.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.w1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503970
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.bx1', '16.cj1', '16.cl1', '16.cm1', '16.co1', '16.cp1'], 'contains': ['64.c1', '64.e1', '64.i1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1516, -1, 1519, -1], 'generators': [240, 4], 'label': '256.26547.32.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.x1', 'projective_image': '128.1755', '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: 64503971
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.r1', '16.bu1', '16.ch1', '16.ck2', '16.co1', '16.cq1'], 'contains': ['64.e1', '64.l1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1374, -1, 1377, -1], 'generators': [19, 4], 'label': '256.26547.32.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.y1', 'projective_image': '128.1755', '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': '8.3'}
  • id: 64503972
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.cp1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.t1', '16.cg1', '16.ch1', '16.cn1', '16.cp1'], 'contains': ['64.e1', '64.w1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [724, -1, 726, -1], 'generators': [218, 128], 'label': '256.26547.32.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '32.z1', 'projective_image': '128.1755', '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: 64503973
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1', '16.bw1', '16.bx1', '16.cq1', '16.cr1'], 'contains': ['64.e1', '64.j1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3018, -1, 3026, -1], 'generators': [4, 208], 'label': '256.26547.32.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.ba1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503974
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.m1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 16, 'centralizer': '64.c1', 'complements': ['64.t1', '64.x1'], 'conjugacy_class_count': 2, 'contained_in': ['2.e1', '2.g1'], 'contains': ['8.j1', '8.k1'], 'core': '4.m1', 'coset_action_label': None, 'count': 2, 'diagramx': [4790, 7509, 4802, 7573], 'generators': [2, 40], 'label': '256.26547.4.m1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1', 'normal_contained_in': ['2.e1', '2.g1'], 'normal_contains': ['8.j1', '8.k1'], 'normalizer': '1.a1', 'old_label': '4.m1', 'projective_image': '128.1755', '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': '64.138'}
  • id: 64503975
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.ba1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.ba1', '16.cs1', '16.ct1'], 'contains': ['64.f1', '64.g1', '64.x1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6098, -1, 6112, -1], 'generators': [1, 28, 128], 'label': '256.26547.32.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bs1', 'old_label': '32.bb1', 'projective_image': '128.1755', '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': '2.1'}
  • id: 64503976
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bb1', '16.ci1', '16.cs1'], 'contains': ['64.b1', '64.f1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5205, -1, 5217, -1], 'generators': [5, 224], 'label': '256.26547.32.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1', 'old_label': '32.bc1', 'projective_image': '128.1755', '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: 64503977
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bb1', '16.cj1', '16.ct1'], 'contains': ['64.c1', '64.f1'], 'core': '64.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [5130, -1, 5141, -1], 'generators': [1, 240], 'label': '256.26547.32.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1', 'old_label': '32.bd1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503978
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bd1', '16.ci1', '16.cj1'], 'contains': ['64.f1', '64.i1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3461, -1, 3469, -1], 'generators': [5, 116], 'label': '256.26547.32.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '32.be1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503979
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bf1', '16.cs1', '16.ct1'], 'contains': ['64.f1', '64.k1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5932, -1, 5946, -1], 'generators': [5, 188], 'label': '256.26547.32.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bs1', 'old_label': '32.bf1', 'projective_image': '128.1755', '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: 64503980
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1', '16.by1', '16.cs1'], 'contains': ['64.b1', '64.g1', '64.k1'], 'core': '64.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5454, -1, 5467, -1], 'generators': [28, 224], 'label': '256.26547.32.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1', 'old_label': '32.bg1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503981
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1', '16.bz1', '16.ct1'], 'contains': ['64.c1', '64.g1', '64.k1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [5313, -1, 5325, -1], 'generators': [204, 240], 'label': '256.26547.32.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1', 'old_label': '32.bh1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503982
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '16.by1', '16.bz1', '16.cu1', '16.cv1'], 'contains': ['64.g1', '64.j1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4312, -1, 4321, -1], 'generators': [28, 208], 'label': '256.26547.32.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '32.bi1', 'projective_image': '128.1755', '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': '8.3'}
  • id: 64503983
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bj1', '16.ca1', '16.ca2', '16.ck1', '16.ck2'], 'contains': ['64.b1', '64.h1', '64.l1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [2175, -1, 2180, -1], 'generators': [3, 224], 'label': '256.26547.32.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bj1', 'projective_image': '128.1755', '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': '2.1'}
  • id: 64503984
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.bk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.bk1', '16.bu1', '16.bv1', '16.ck2', '16.cl1', '16.cw1', '16.cy1'], 'contains': ['64.h1', '64.i1', '64.l1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1807, -1, 1812, -1], 'generators': [3, 164], 'label': '256.26547.32.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bk1', 'projective_image': '128.1755', '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: 64503985
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.q1', '8.r1', '8.z1', '8.be1'], 'core': '8.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2265, -1, 2271, -1], 'generators': [3, 218, 32], 'label': '256.26547.4.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.n1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 64503986
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.ca1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bl1', '16.ca1', '16.cb1', '16.cq1', '16.cr1', '16.cw1', '16.cy1'], 'contains': ['64.h1', '64.j1', '64.l1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2608, -1, 2614, -1], 'generators': [7, 208], 'label': '256.26547.32.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bl1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503987
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1', '16.cb1', '16.cc1', '16.cl1', '16.cm1'], 'contains': ['64.c1', '64.h1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1991, -1, 1996, -1], 'generators': [3, 240], 'label': '256.26547.32.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bm1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503988
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bk1', '16.bv1', '16.ck1', '16.cm1', '16.cy1'], 'contains': ['64.h1', '64.i1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1699, -1, 1703, -1], 'generators': [7, 164], 'label': '256.26547.32.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bn1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503989
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.ca2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bl1', '16.ca2', '16.cc1', '16.cr1', '16.cu1', '16.cx1', '16.cy1'], 'contains': ['64.h1', '64.j1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3094, -1, 3101, -1], 'generators': [3, 208], 'label': '256.26547.32.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '32.bo1', 'projective_image': '128.1755', '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': '8.3'}
  • id: 64503990
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1', '16.cb1', '16.ce1', '16.cl1', '16.co1'], 'contains': ['64.c1', '64.l1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2066, -1, 2071, -1], 'generators': [215, 240], 'label': '256.26547.32.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bp1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503991
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bk1', '16.bu1', '16.ck1', '16.co1', '16.cw1'], 'contains': ['64.i1', '64.l1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1916, -1, 1921, -1], 'generators': [23, 164], 'label': '256.26547.32.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.bq1', 'projective_image': '128.1755', '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': '4.2'}
  • id: 64503992
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1', '16.bw1', '16.bx1', '16.cw1', '16.cy1'], 'contains': ['64.i1', '64.j1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3169, -1, 3176, -1], 'generators': [164, 208], 'label': '256.26547.32.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '32.br1', 'projective_image': '128.1755', '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: 64503993
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1', '16.by1', '16.bz1', '16.cx1', '16.cz1'], 'contains': ['64.j1', '64.k1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4236, -1, 4246, -1], 'generators': [188, 208], 'label': '256.26547.32.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '32.bs1', 'projective_image': '128.1755', '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': '8.3'}
  • id: 64503994
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bt1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.ca2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bl1', '16.ca2', '16.ce1', '16.cq1', '16.cv1', '16.cw1', '16.cz1'], 'contains': ['64.j1', '64.l1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3244, -1, 3252, -1], 'generators': [19, 208], 'label': '256.26547.32.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '32.bt1', 'projective_image': '128.1755', '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': '8.3'}
  • id: 64503995
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.br1', '16.cd1', '16.cf1', '16.cu1', '16.cv1', '16.cx1', '16.cz1'], 'contains': ['64.j1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3886, -1, 3894, -1], 'generators': [79], 'label': '256.26547.32.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '32.bu1', 'projective_image': '128.1755', '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: 64503996
    {'ambient': '256.26547', 'aut_centralizer_order': 2, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '256.56092', 'aut_weyl_index': 16, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1'], 'contains': ['8.a1', '8.o1', '8.p1', '8.s1', '8.s2', '8.u1', '8.u2', '8.x1', '8.y1', '8.bb1', '8.bc1', '8.bh1', '8.bi1', '8.bq1', '8.br1'], 'core': '8.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8342, -1, 8362, -1], 'generators': [1, 8, 32, 4], 'label': '256.26547.4.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.o1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64503997
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.l1', '16.da1'], 'contains': ['64.m1', '64.o1', '64.s1'], 'core': '256.a1', 'coset_action_label': '32T2629', 'count': 32, 'diagramx': [8848, -1, 8869, -1], 'generators': [1, 32], 'label': '256.26547.32.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1', 'old_label': '32.bv1', 'projective_image': '256.26547', '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': '4.2'}
  • id: 64503998
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '32.bw1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.o1', '16.da1'], 'contains': ['64.m1', '64.q1', '64.r1'], 'core': '256.a1', 'coset_action_label': '32T2627', 'count': 8, 'diagramx': [9333, -1, 9355, -1], 'generators': [8, 32], 'label': '256.26547.32.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.q1', 'old_label': '32.bw1', 'projective_image': '256.26547', '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': '2.1'}
  • id: 64503999
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.p1', '16.db1'], 'contains': ['64.n1', '64.o2', '64.s1'], 'core': '256.a1', 'coset_action_label': '32T3196', 'count': 32, 'diagramx': [8339, -1, 8359, -1], 'generators': [1, 212], 'label': '256.26547.32.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1', 'old_label': '32.bx1', 'projective_image': '256.26547', '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': '4.2'}
  • id: 64504000
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.by1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '16.db1'], 'contains': ['64.n1', '64.o1', '64.o2', '64.u1'], 'core': '256.a1', 'coset_action_label': '32T3191', 'count': 32, 'diagramx': [7872, -1, 7890, -1], 'generators': [1, 4, 16], 'label': '256.26547.32.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1', 'old_label': '32.by1', 'projective_image': '256.26547', '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: 64504001
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '32.bz1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.q1', '16.db1'], 'contains': ['64.n1', '64.p1', '64.q1'], 'core': '256.a1', 'coset_action_label': '32T3192', 'count': 16, 'diagramx': [8037, -1, 8056, -1], 'generators': [8, 4], 'label': '256.26547.32.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1', 'old_label': '32.bz1', 'projective_image': '256.26547', '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': '4.2'}
  • id: 64504002
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.ca1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.u1', '16.db1'], 'contains': ['64.o2', '64.p1', '64.s1'], 'core': '256.a1', 'coset_action_label': '32T3193', 'count': 32, 'diagramx': [8414, -1, 8434, -1], 'generators': [5, 28], 'label': '256.26547.32.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1', 'old_label': '32.ca1', 'projective_image': '256.26547', '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: 64504003
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.cb1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.v1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.v1', '16.da1', '16.db1'], 'contains': ['64.o1', '64.q1', '64.s1'], 'core': '256.a1', 'coset_action_label': '32T2628', 'count': 32, 'diagramx': [8956, -1, 8977, -1], 'generators': [1, 8], 'label': '256.26547.32.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1', 'old_label': '32.cb1', 'projective_image': '256.26547', '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: 64504004
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.ba1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.ba1', '16.db1'], 'contains': ['64.o1', '64.o2', '64.p1', '64.x1'], 'core': '256.a1', 'coset_action_label': '32T3195', 'count': 32, 'diagramx': [8259, -1, 8278, -1], 'generators': [1, 28, 16], 'label': '256.26547.32.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1', 'old_label': '32.cc1', 'projective_image': '256.26547', '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': '2.1'}
  • id: 64504005
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.cd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.bc1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.bc1', '16.db1'], 'contains': ['64.o2', '64.q1'], 'core': '256.a1', 'coset_action_label': '32T3194', 'count': 16, 'diagramx': [8631, -1, 8651, -1], 'generators': [5, 8], 'label': '256.26547.32.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '32.cd1', 'projective_image': '256.26547', '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': '4.2'}
  • id: 64504006
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.ce1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.be1', '16.da1'], 'contains': ['64.o1', '64.r1'], 'core': '256.a1', 'coset_action_label': '32T2631', 'count': 16, 'diagramx': [9559, -1, 9603, -1], 'generators': [1, 40], 'label': '256.26547.32.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1', 'old_label': '32.ce1', 'projective_image': '256.26547', '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': '4.2'}
  • id: 64504007
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '512.7538135', 'aut_weyl_index': 8, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1'], 'contains': ['8.c1', '8.s1', '8.s2', '8.t1', '8.bj1', '8.bk1', '8.bp1', '8.bs1', '8.bu1'], 'core': '8.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [7112, -1, 7127, -1], 'generators': [1, 28, 32, 208], 'label': '256.26547.4.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.p1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504008
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '32.cf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.bs1', '16.da1'], 'contains': ['64.r1', '64.s1'], 'core': '256.a1', 'coset_action_label': '32T2630', 'count': 16, 'diagramx': [9727, -1, 9782, -1], 'generators': [209, 40], 'label': '256.26547.32.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1', 'old_label': '32.cf1', 'projective_image': '256.26547', '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': '4.2'}
  • id: 64504009
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '32.cg1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.cg1'], 'contains': ['64.u1', '64.v1', '64.w1'], 'core': '256.a1', 'coset_action_label': '32T4770', 'count': 128, 'diagramx': [615, -1, 617, -1], 'generators': [211, 218], 'label': '256.26547.32.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.cg1', 'old_label': '32.cg1', 'projective_image': '256.26547', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64504010
    {'ambient': '256.26547', 'aut_centralizer_order': 2048, 'aut_label': '64.a1', 'aut_quo_index': 192, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.b1', '32.c1', '32.d1', '32.e1', '32.f1', '32.g1', '32.h1', '32.i1', '32.j1', '32.k1', '32.l1'], 'contains': ['128.a1', '128.b1'], 'core': '64.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6012, 4416, 6026, 4454], 'generators': [16, 128], 'label': '256.26547.64.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1', '32.c1', '32.d1', '32.e1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '128.1755', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64504011
    {'ambient': '256.26547', 'aut_centralizer_order': 2048, 'aut_label': '64.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1', '32.q1', '32.w1', '32.bc1', '32.bg1', '32.bj1'], 'contains': ['128.a1'], 'core': '64.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3569, 4821, 3577, 4862], 'generators': [224], 'label': '256.26547.64.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': ['32.c1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.b1', 'projective_image': '128.1755', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64504012
    {'ambient': '256.26547', 'aut_centralizer_order': 2048, 'aut_label': '64.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.e1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1', '32.r1', '32.x1', '32.bd1', '32.bh1', '32.bm1', '32.bp1'], 'contains': ['128.a1'], 'core': '64.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3302, 5200, 3310, 5244], 'generators': [240], 'label': '256.26547.64.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1', 'normal_contained_in': ['32.c1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.c1', 'projective_image': '128.1755', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.6', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64504013
    {'ambient': '256.26547', 'aut_centralizer_order': 1024, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.m1', '32.n1', '32.o1', '32.p1', '32.q1', '32.r1', '32.s1'], 'contains': ['128.a1', '128.c1'], 'core': '128.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3382, -1, 3390, -1], 'generators': [32, 128], 'label': '256.26547.64.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '64.d1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64504014
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.b1', '32.m1', '32.t1', '32.u1', '32.v1', '32.w1', '32.x1', '32.y1', '32.z1', '32.ba1'], 'contains': ['128.a1', '128.d1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1624, -1, 1628, -1], 'generators': [4, 128], 'label': '256.26547.64.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.e1', 'projective_image': '128.1755', '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: 64504015
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.f1', '32.t1', '32.bb1', '32.bc1', '32.bd1', '32.be1', '32.bf1'], 'contains': ['128.a1', '128.e1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5205, -1, 5217, -1], 'generators': [1, 128], 'label': '256.26547.64.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1', 'old_label': '64.f1', 'projective_image': '128.1755', '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': '2.1'}
  • id: 64504016
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1', '32.n1', '32.bb1', '32.bg1', '32.bh1', '32.bi1'], 'contains': ['128.a1', '128.f1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5425, -1, 5436, -1], 'generators': [28, 128], 'label': '256.26547.64.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1', 'old_label': '64.g1', 'projective_image': '128.1755', '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: 64504017
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.h1', '32.o1', '32.p1', '32.u1', '32.v1', '32.bj1', '32.bk1', '32.bl1', '32.bm1', '32.bn1', '32.bo1'], 'contains': ['128.a1', '128.g1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2203, -1, 2208, -1], 'generators': [3, 128], 'label': '256.26547.64.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.h1', 'projective_image': '128.1755', '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: 64504018
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.55751', 'aut_weyl_index': 16, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1'], 'contains': ['8.d1', '8.t1', '8.u1', '8.u2', '8.bl1', '8.bm1', '8.bo1', '8.bt1', '8.ca1'], 'core': '8.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9392, -1, 9413, -1], 'generators': [1, 8, 32, 208], 'label': '256.26547.4.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.q1', 'projective_image': '128.1755', '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: 64504019
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.d1', '32.m1', '32.w1', '32.x1', '32.be1', '32.bk1', '32.bn1', '32.bq1', '32.br1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2516, -1, 2522, -1], 'generators': [164], 'label': '256.26547.64.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.i1', 'projective_image': '128.1755', '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: 64504020
    {'ambient': '256.26547', 'aut_centralizer_order': 1024, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1', '32.q1', '32.r1', '32.ba1', '32.bi1', '32.bl1', '32.bo1', '32.br1', '32.bs1', '32.bt1', '32.bu1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3463, -1, 3471, -1], 'generators': [208], 'label': '256.26547.64.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '64.j1', 'projective_image': '128.1755', '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: 64504021
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1', '32.n1', '32.bf1', '32.bg1', '32.bh1', '32.bs1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5313, -1, 5325, -1], 'generators': [188], 'label': '256.26547.64.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1', 'old_label': '64.k1', 'projective_image': '128.1755', '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: 64504022
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.h1', '32.o1', '32.s1', '32.u1', '32.y1', '32.bj1', '32.bk1', '32.bl1', '32.bp1', '32.bq1', '32.bt1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2283, -1, 2288, -1], 'generators': [215], 'label': '256.26547.64.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '64.l1', 'projective_image': '128.1755', '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': '2.1'}
  • id: 64504023
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.bv1', '32.bw1'], 'contains': ['128.b1', '128.c1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8208, -1, 8227, -1], 'generators': [32, 16], 'label': '256.26547.64.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.q1', 'old_label': '64.m1', 'projective_image': '256.26547', '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': '2.1'}
  • id: 64504025
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.f1', '32.bv1', '32.by1', '32.cb1', '32.cc1', '32.ce1'], 'contains': ['128.b1', '128.e1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8294, -1, 8313, -1], 'generators': [1, 16], 'label': '256.26547.64.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1', 'old_label': '64.o1', 'projective_image': '256.26547', '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': '2.1'}
  • id: 64504026
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '64.o2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.f1', '32.bx1', '32.by1', '32.ca1', '32.cc1', '32.cd1'], 'contains': ['128.b1', '128.e1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8122, -1, 8141, -1], 'generators': [1, 144], 'label': '256.26547.64.o2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1', 'old_label': '64.o2', 'projective_image': '256.26547', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64504027
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bs1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.g1', '32.bz1', '32.ca1', '32.cc1'], 'contains': ['128.b1', '128.f1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8037, -1, 8056, -1], 'generators': [28, 16], 'label': '256.26547.64.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1', 'old_label': '64.p1', 'projective_image': '256.26547', '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': '2.1'}
  • id: 64504028
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.i1', '32.bw1', '32.bz1', '32.cb1', '32.cd1'], 'contains': ['128.b1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8578, -1, 8597, -1], 'generators': [8], 'label': '256.26547.64.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '64.q1', 'projective_image': '256.26547', '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: 64504029
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1'], 'contains': ['8.c1', '8.v1', '8.w1', '8.bv1', '8.by1', '8.cf1', '8.cg1', '8.ch1'], 'core': '8.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [3477, -1, 3486, -1], 'generators': [3, 28, 32, 16], 'label': '256.26547.4.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '4.r1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504030
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1', '32.bw1', '32.ce1', '32.cf1'], 'contains': ['128.b1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9333, -1, 9355, -1], 'generators': [40], 'label': '256.26547.64.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.q1', 'old_label': '64.r1', 'projective_image': '256.26547', '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: 64504031
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bi1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.k1', '32.bv1', '32.bx1', '32.ca1', '32.cb1', '32.cf1'], 'contains': ['128.b1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8414, -1, 8434, -1], 'generators': [209], 'label': '256.26547.64.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1', 'old_label': '64.s1', 'projective_image': '256.26547', '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': '2.1'}
  • id: 64504032
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.ca1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1'], 'contains': ['128.c1', '128.g1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2721, -1, 2728, -1], 'generators': [3, 32], 'label': '256.26547.64.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.ca1', 'old_label': '64.t1', 'projective_image': '256.26547', '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': '1.1'}
  • id: 64504033
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '64.u1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.t1', '32.by1', '32.cg1'], 'contains': ['128.d1', '128.e1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [1539, -1, 1542, -1], 'generators': [1, 4], 'label': '256.26547.64.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.z1', 'old_label': '64.u1', 'projective_image': '256.26547', '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: 64504034
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.ck2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.v1', '32.cg1'], 'contains': ['128.d1', '128.g1'], 'core': '256.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1313, -1, 1318, -1], 'generators': [3, 4], 'label': '256.26547.64.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ci1', 'old_label': '64.v1', 'projective_image': '256.26547', '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: 64504035
    {'ambient': '256.26547', 'aut_centralizer_order': 64, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.cp1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.z1', '32.cg1'], 'contains': ['128.d1'], 'core': '256.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [724, -1, 726, -1], 'generators': [218], 'label': '256.26547.64.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.cj1', 'old_label': '64.w1', 'projective_image': '256.26547', '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: 64504036
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.ba1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.bb1', '32.cc1'], 'contains': ['128.e1', '128.f1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [6098, -1, 6112, -1], 'generators': [1, 28], 'label': '256.26547.64.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.ba1', 'old_label': '64.x1', 'projective_image': '256.26547', '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': '1.1'}
  • id: 64504037
    {'ambient': '256.26547', 'aut_centralizer_order': 4096, 'aut_label': '128.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.c1', '64.d1', '64.e1', '64.f1', '64.g1', '64.h1', '64.i1', '64.j1', '64.k1', '64.l1'], 'contains': ['256.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3424, 4821, 3430, 4862], 'generators': [128], 'label': '256.26547.128.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': '128.1755', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.1755', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64504038
    {'ambient': '256.26547', 'aut_centralizer_order': 2048, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.m1', '64.n1', '64.o1', '64.o2', '64.p1', '64.q1', '64.r1', '64.s1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8165, -1, 8184, -1], 'generators': [16], 'label': '256.26547.128.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '128.b1', 'projective_image': '256.26547', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64504039
    {'ambient': '256.26547', 'aut_centralizer_order': 1024, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '4.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1', '64.m1', '64.t1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3498, -1, 3505, -1], 'generators': [32], 'label': '256.26547.128.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1', 'old_label': '128.c1', 'projective_image': '256.26547', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64504040
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2323', 'aut_weyl_index': 32, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1'], 'contains': ['8.d1', '8.v1', '8.w1', '8.bw1', '8.bx1'], 'core': '8.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [4081, -1, 4090, -1], 'generators': [3, 8, 32], 'label': '256.26547.4.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '4.s1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64504041
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '4.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.e1', '64.n1', '64.u1', '64.v1', '64.w1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1582, -1, 1585, -1], 'generators': [4], 'label': '256.26547.128.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '128.d1', 'projective_image': '256.26547', '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: 64504042
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.f1', '64.o1', '64.o2', '64.u1', '64.x1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5814, -1, 5796, -1], 'generators': [1], 'label': '256.26547.128.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1', 'old_label': '128.e1', 'projective_image': '256.26547', '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: 64504043
    {'ambient': '256.26547', 'aut_centralizer_order': 512, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.bs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.g1', '64.p1', '64.x1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5566, -1, 5594, -1], 'generators': [28], 'label': '256.26547.128.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bs1', 'old_label': '128.f1', 'projective_image': '256.26547', '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: 64504044
    {'ambient': '256.26547', 'aut_centralizer_order': 256, 'aut_label': '128.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.cd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.h1', '64.t1', '64.v1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2462, -1, 2468, -1], 'generators': [3], 'label': '256.26547.128.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.cd1', 'old_label': '128.g1', 'projective_image': '256.26547', '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: 64504045
    {'ambient': '256.26547', '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'], 'contains': [], 'core': '256.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3498, 4821, 3505, 4862], 'generators': [], 'label': '256.26547.256.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1', 'normal_contained_in': ['128.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '256.a1', 'projective_image': '256.26547', '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: 64504046
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['8.f1', '8.x1', '8.y1', '8.ba1', '8.bd1', '8.bh1', '8.bi1', '8.bj1', '8.bl1', '8.bu1', '8.ca1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [8026, -1, 8044, -1], 'generators': [209, 8, 240, 4], 'label': '256.26547.4.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.t1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504047
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 16, 'centralizer': '64.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.e1', '8.z1', '8.bf1', '8.bg1', '8.ci1', '8.cj1', '8.ck1'], 'core': '8.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [1162, -1, 1164, -1], 'generators': [7, 218, 164, 16], 'label': '256.26547.4.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.u1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 64504048
    {'ambient': '256.26547', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1024.dlr', 'aut_weyl_index': 4, 'centralizer': '128.a1', 'complements': ['128.f1', '128.e1', '128.g1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.e1', '4.g1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4418, 2891, 4428, 2915], 'generators': [1, 218, 32], 'label': '256.26547.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '4.e1', '4.g1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '128.1755', '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': '128.1755'}
  • id: 64504049
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['8.e1', '8.ba1', '8.bb1', '8.bc1', '8.bd1', '8.bj1', '8.bl1', '8.bq1', '8.br1', '8.bs1', '8.bt1'], 'core': '8.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [7699, -1, 7716, -1], 'generators': [1, 8, 240, 4], 'label': '256.26547.4.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.v1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504050
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55999', 'aut_weyl_index': 16, 'centralizer': '64.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.f1', '8.be1', '8.bf1', '8.bg1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [1721, -1, 1725, -1], 'generators': [3, 218, 164], 'label': '256.26547.4.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.w1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504051
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 8, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1'], 'contains': ['8.m1', '8.bh1', '8.bk1', '8.bn1', '8.bo1', '8.bq1'], 'core': '8.m1', 'coset_action_label': None, 'count': 2, 'diagramx': [7849, -1, 7867, -1], 'generators': [1, 28, 164, 208], 'label': '256.26547.4.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.x1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.x1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504052
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '512.6407063', 'aut_weyl_index': 8, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1'], 'contains': ['8.n1', '8.bi1', '8.bm1', '8.bn1', '8.bp1', '8.br1'], 'core': '8.n1', 'coset_action_label': None, 'count': 2, 'diagramx': [7286, -1, 7302, -1], 'generators': [1, 8, 164, 208], 'label': '256.26547.4.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.y1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.y1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504053
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1'], 'contains': ['8.m1', '8.bv1', '8.bx1', '8.bz1', '8.cb1'], 'core': '8.m1', 'coset_action_label': None, 'count': 2, 'diagramx': [3866, -1, 3875, -1], 'generators': [3, 28, 164], 'label': '256.26547.4.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '4.z1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.z1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504054
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '4.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1'], 'contains': ['8.n1', '8.bw1', '8.by1', '8.bz1', '8.cb1'], 'core': '8.n1', 'coset_action_label': None, 'count': 2, 'diagramx': [3663, -1, 3671, -1], 'generators': [3, 8, 164], 'label': '256.26547.4.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '4.ba1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ba1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504055
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 32, 'centralizer': '64.a1', 'complements': ['32.cg1'], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.n1', '4.o1'], 'contains': ['16.a1', '16.c1', '16.e1', '16.l1', '16.w1'], 'core': '8.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6007, 502, 6021, 507], 'generators': [1, 32, 4], 'label': '256.26547.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.a1', '16.c1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 64504056
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '32.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.b1', '16.d1', '16.f1', '16.i1', '16.bw1', '16.bx1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4739, 3169, 4750, 3196], 'generators': [32, 4, 208, 16], 'label': '256.26547.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.b1', '16.d1', '16.f1', '16.i1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504057
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '32.c1', 'complements': ['32.cg1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.p1', '4.r1'], 'contains': ['16.b1', '16.g1', '16.k1', '16.m1', '16.bg1', '16.by1', '16.bz1'], 'core': '8.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5078, 9524, 5090, 9605], 'generators': [28, 32, 208, 16], 'label': '256.26547.8.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.b1', '16.g1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504058
    {'ambient': '256.26547', 'aut_centralizer_order': 128, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '8.d1', 'complements': ['32.cg1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.q1', '4.s1'], 'contains': ['16.b1', '16.h1', '16.j1', '16.o1', '16.bm1'], 'core': '8.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6180, 8182, 6194, 8252], 'generators': [8, 32, 208], 'label': '256.26547.8.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.b1', '16.h1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64504059
    {'ambient': '256.26547', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '64.a1', 'complements': ['128.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.h1', '4.i1', '4.o1', '4.p1', '4.q1', '4.t1', '4.v1', '4.x1', '4.y1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7538, 6589, 7555, 6645], 'generators': [1, 8, 32, 208, 4], 'label': '256.26547.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.h1', '4.i1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '128.1755', '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': '64.202'}
  • id: 64504060
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 32, 'centralizer': '32.b1', 'complements': ['32.cg1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.u1', '4.v1'], 'contains': ['16.c1', '16.d1', '16.bb1', '16.bd1', '16.ci1', '16.cj1'], 'core': '8.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [4909, 2312, 4920, 2332], 'generators': [1, 240, 4, 16], 'label': '256.26547.8.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.c1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 64504061
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 32, 'centralizer': '32.d1', 'complements': ['32.cg1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.t1', '4.w1'], 'contains': ['16.d1', '16.e1', '16.bn1', '16.bq1'], 'core': '8.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [5824, 1428, 5837, 1440], 'generators': [209, 240, 4], 'label': '256.26547.8.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.d1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504062
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.g1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 32, 'centralizer': '64.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.f1', '4.g1', '4.h1', '4.i1'], 'contains': ['16.c1', '16.e1', '16.f1', '16.p1', '16.x1'], 'core': '8.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [5640, 5258, 5653, 5302], 'generators': [1, 4, 208], 'label': '256.26547.8.g1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': ['4.a1', '4.f1', '4.g1', '4.h1', '4.i1'], 'normal_contains': ['16.c1', '16.e1', '16.f1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 64504063
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '32.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.h1', '4.j1', '4.k1'], 'contains': ['16.f1', '16.g1', '16.h1', '16.q1'], 'core': '8.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [5406, 7041, 5418, 7101], 'generators': [8, 4, 208], 'label': '256.26547.8.h1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1', 'normal_contained_in': ['4.b1', '4.h1', '4.j1', '4.k1'], 'normal_contains': ['16.f1', '16.g1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': '128.1755', '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': '32.27'}
  • id: 64504083
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.h1', '4.o1', '4.t1'], 'contains': ['16.e1', '16.p1', '16.q1', '16.u1', '16.v1', '16.bi1', '16.bp1'], 'core': '16.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [8923, -1, 8944, -1], 'generators': [209, 8, 4], 'label': '256.26547.8.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.x1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504064
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.i1', 'aut_quo_index': 42, 'aut_stab_index': 2, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '64.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.f1', '4.j1', '4.l1'], 'contains': ['16.f1', '16.r1', '16.bl1', '16.cq1', '16.cr1'], 'core': '8.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [2776, 3905, 2782, 3939], 'generators': [3, 4, 208, 16], 'label': '256.26547.8.i1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1', 'normal_contained_in': ['4.c1', '4.f1', '4.j1', '4.l1'], 'normal_contains': ['16.f1'], 'normalizer': '1.a1', 'old_label': '8.i1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 64504065
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.j1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '32.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.i1', '4.l1', '4.m1'], 'contains': ['16.f1', '16.j1', '16.k1', '16.s1'], 'core': '8.j1', 'coset_action_label': None, 'count': 1, 'diagramx': [5310, 6557, 5322, 6612], 'generators': [40, 4, 208], 'label': '256.26547.8.j1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1', 'normal_contained_in': ['4.b1', '4.i1', '4.l1', '4.m1'], 'normal_contains': ['16.f1', '16.j1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.j1', 'projective_image': '128.1755', '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': '32.27'}
  • id: 64504066
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.k1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '64.c1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.f1', '4.g1', '4.k1', '4.m1'], 'contains': ['16.f1', '16.t1'], 'core': '8.k1', 'coset_action_label': None, 'count': 4, 'diagramx': [4592, 6015, 4603, 6066], 'generators': [218, 208], 'label': '256.26547.8.k1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1', 'normal_contained_in': ['4.d1', '4.f1', '4.g1', '4.k1', '4.m1'], 'normal_contains': ['16.f1'], 'normalizer': '1.a1', 'old_label': '8.k1', 'projective_image': '128.1755', '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': '64.138'}
  • id: 64504067
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': 42, 'aut_stab_index': 2, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '64.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '4.g1', '4.j1', '4.l1'], 'contains': ['16.f1', '16.br1'], 'core': '8.l1', 'coset_action_label': None, 'count': 2, 'diagramx': [4475, 4500, 4485, 4538], 'generators': [219, 4], 'label': '256.26547.8.l1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1', 'normal_contained_in': ['4.e1', '4.g1', '4.j1', '4.l1'], 'normal_contains': ['16.f1'], 'normalizer': '1.a1', 'old_label': '8.l1', 'projective_image': '128.1755', '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': '64.138'}
  • id: 64504068
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.m1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '32.c1', 'complements': ['32.cg1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.x1', '4.z1'], 'contains': ['16.g1', '16.i1', '16.j1', '16.bh1'], 'core': '8.m1', 'coset_action_label': None, 'count': 1, 'diagramx': [5502, 8841, 5514, 8915], 'generators': [28, 164, 208], 'label': '256.26547.8.m1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.g1', '16.i1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.m1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504069
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '32.c1', 'complements': ['32.cg1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.y1', '4.ba1'], 'contains': ['16.h1', '16.i1', '16.k1', '16.bo1'], 'core': '8.n1', 'coset_action_label': None, 'count': 1, 'diagramx': [5214, 7525, 5226, 7589], 'generators': [8, 164, 208], 'label': '256.26547.8.n1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.h1', '16.i1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.n1', 'projective_image': '128.1755', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.n1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504070
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.dkd', 'aut_weyl_index': 4, 'centralizer': '64.b1', 'complements': ['128.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.e1', '4.j1', '4.l1', '4.r1', '4.s1', '4.z1', '4.ba1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4146, 3954, 4155, 3987], 'generators': [3, 8, 32, 4], 'label': '256.26547.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.e1', '4.j1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '128.1755', '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': '64.138'}
  • id: 64504071
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 32, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.o1'], 'contains': ['16.a1', '16.l1', '16.p1', '16.bd1', '16.bq1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6832, -1, 6848, -1], 'generators': [1, 32, 212], 'label': '256.26547.8.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.o1', 'projective_image': '128.1755', '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: 64504072
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.o1'], 'contains': ['16.a1', '16.m1', '16.o1', '16.q1', '16.s1', '16.bh1', '16.bo1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6940, -1, 6956, -1], 'generators': [8, 32, 4], 'label': '256.26547.8.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.p1', 'projective_image': '128.1755', '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: 64504073
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.n1'], 'contains': ['16.a1', '16.n1', '16.r1', '16.bk1', '16.bu1', '16.bv1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1839, -1, 1843, -1], 'generators': [3, 32, 4, 16], 'label': '256.26547.8.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.q1', 'projective_image': '128.1755', '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': '32.27'}
  • id: 64504074
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '64.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '4.n1'], 'contains': ['16.a1', '16.t1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2512, -1, 2649, -1], 'generators': [218, 32], 'label': '256.26547.8.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.r1', 'projective_image': '128.1755', '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': '32.27'}
  • id: 64504075
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 32, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.o1', '4.p1'], 'contains': ['16.l1', '16.m1', '16.u1', '16.bf1', '16.bt1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8411, -1, 8431, -1], 'generators': [5, 28, 32], 'label': '256.26547.8.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.s1', 'projective_image': '128.1755', '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': '32.51'}
  • id: 64504076
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.s2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 32, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.o1', '4.p1'], 'contains': ['16.l1', '16.m1', '16.z1', '16.ba1', '16.bi1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8273, -1, 8292, -1], 'generators': [1, 28, 32], 'label': '256.26547.8.s2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.s2', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504077
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.p1', '4.q1'], 'contains': ['16.b1', '16.l1', '16.x1', '16.bb1', '16.bn1'], 'core': '16.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7057, -1, 7074, -1], 'generators': [1, 32, 208], 'label': '256.26547.8.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.t1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504078
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.o1', '4.q1'], 'contains': ['16.l1', '16.o1', '16.v1', '16.be1', '16.bs1', '16.da1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9896, -1, 9920, -1], 'generators': [1, 8, 32, 128], 'label': '256.26547.8.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.u1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504079
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.u2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 32, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.o1', '4.q1'], 'contains': ['16.l1', '16.o1', '16.y1', '16.bc1', '16.bp1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9750, -1, 9774, -1], 'generators': [5, 8, 32], 'label': '256.26547.8.u2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.u2', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504080
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.r1', '4.s1'], 'contains': ['16.b1', '16.n1', '16.bj1', '16.bl1', '16.ca1', '16.ca2', '16.cb1', '16.cc1', '16.ce1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3040, -1, 3047, -1], 'generators': [3, 32, 208, 16], 'label': '256.26547.8.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.v1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64504081
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.dnj', 'aut_weyl_index': 4, 'centralizer': '64.c1', 'complements': ['128.e1', '128.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.d1', '4.k1', '4.m1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [4925, 7509, 4937, 7573], 'generators': [2, 8, 32], 'label': '256.26547.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.d1', '4.k1', '4.m1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '128.1755', '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': '64.138'}
  • id: 64504082
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '4.r1', '4.s1'], 'contains': ['16.b1', '16.br1', '16.cd1', '16.cf1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3844, -1, 3853, -1], 'generators': [219, 32, 16], 'label': '256.26547.8.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.w1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64504084
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.o1', '4.t1'], 'contains': ['16.e1', '16.p1', '16.s1', '16.y1', '16.z1', '16.bs1', '16.bt1'], 'core': '16.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [8816, -1, 8836, -1], 'generators': [209, 40, 4], 'label': '256.26547.8.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.y1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504085
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '64.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.f1', '4.n1', '4.u1'], 'contains': ['16.c1', '16.r1', '16.t1', '16.cg1', '16.ch1'], 'core': '16.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [1254, -1, 1256, -1], 'generators': [7, 218, 16], 'label': '256.26547.8.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.z1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 64504086
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.t1', '4.v1'], 'contains': ['16.d1', '16.p1', '16.w1', '16.bb1', '16.bn1'], 'core': '16.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [6725, -1, 6741, -1], 'generators': [1, 164, 212], 'label': '256.26547.8.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.ba1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504087
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.h1', '4.o1', '4.v1'], 'contains': ['16.c1', '16.p1', '16.q1', '16.u1', '16.v1', '16.ba1', '16.bc1', '16.db1'], 'core': '16.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [8542, -1, 8562, -1], 'generators': [1, 8, 4, 128], 'label': '256.26547.8.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bb1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64504088
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.o1', '4.v1'], 'contains': ['16.c1', '16.p1', '16.s1', '16.y1', '16.z1', '16.be1', '16.bf1'], 'core': '16.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [8092, -1, 8111, -1], 'generators': [1, 40, 4], 'label': '256.26547.8.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bc1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504089
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.t1', '4.v1'], 'contains': ['16.d1', '16.q1', '16.s1', '16.bg1', '16.bh1', '16.bm1', '16.bo1'], 'core': '16.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [6595, -1, 6610, -1], 'generators': [8, 240, 4], 'label': '256.26547.8.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bd1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64504090
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '64.i1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.f1', '4.n1', '4.w1'], 'contains': ['16.e1', '16.r1', '16.t1'], 'core': '16.e1', 'coset_action_label': None, 'count': 16, 'diagramx': [1721, -1, 1725, -1], 'generators': [3, 218], 'label': '256.26547.8.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.be1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64504091
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.w1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.u1', '4.w1'], 'contains': ['16.d1', '16.r1', '16.bj1', '16.bk1', '16.ck1', '16.ck2', '16.cl1', '16.cm1', '16.co1'], 'core': '16.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [1431, -1, 1435, -1], 'generators': [3, 240, 4, 16], 'label': '256.26547.8.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bf1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64504092
    {'ambient': '256.26547', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 8, 'centralizer': '128.a1', 'complements': ['128.c1', '128.e1', '128.g1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.f1', '4.g1', '4.h1', '4.j1', '4.k1'], 'core': '2.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [4747, 5647, 4758, 5695], 'generators': [1, 2, 8], 'label': '256.26547.2.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.f1', '4.g1', '4.h1', '4.j1', '4.k1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '128.1755', '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': '128.1755'}
  • id: 64504093
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '4.u1', '4.w1'], 'contains': ['16.d1', '16.t1', '16.cn1', '16.cp1'], 'core': '16.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [1070, -1, 1072, -1], 'generators': [218, 164, 16], 'label': '256.26547.8.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bg1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64504094
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.o1', '4.t1', '4.x1'], 'contains': ['16.u1', '16.w1', '16.y1', '16.bh1', '16.bi1', '16.bq1', '16.bs1'], 'core': '32.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [9212, -1, 9234, -1], 'generators': [5, 28, 164], 'label': '256.26547.8.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bh1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64504095
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.bi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.o1', '4.t1', '4.y1'], 'contains': ['16.v1', '16.w1', '16.z1', '16.bo1', '16.bp1', '16.bq1', '16.bt1'], 'core': '32.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [7908, -1, 7926, -1], 'generators': [1, 8, 164], 'label': '256.26547.8.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bi1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64504096
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.p1', '4.t1', '4.v1'], 'contains': ['16.u1', '16.z1', '16.bb1', '16.bg1', '16.bn1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [7272, -1, 7289, -1], 'generators': [5, 28, 240], 'label': '256.26547.8.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bj1', 'projective_image': '128.1755', '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': '32.51'}
  • id: 64504097
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.bk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 32, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.h1', '4.p1', '4.x1'], 'contains': ['16.g1', '16.u1', '16.x1', '16.ba1', '16.bi1'], 'core': '16.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [7422, -1, 7440, -1], 'generators': [1, 28, 208], 'label': '256.26547.8.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bk1', 'projective_image': '128.1755', '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': '32.51'}
  • id: 64504098
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.q1', '4.t1', '4.v1'], 'contains': ['16.v1', '16.y1', '16.bb1', '16.bm1', '16.bn1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9331, -1, 9353, -1], 'generators': [1, 8, 240], 'label': '256.26547.8.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bl1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504099
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.202', 'aut_weyl_index': 64, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.h1', '4.q1', '4.y1'], 'contains': ['16.h1', '16.v1', '16.x1', '16.bc1', '16.bp1'], 'core': '16.h1', 'coset_action_label': None, 'count': 4, 'diagramx': [8696, -1, 8716, -1], 'generators': [1, 8, 208], 'label': '256.26547.8.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bm1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504100
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 32, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.x1', '4.y1'], 'contains': ['16.i1', '16.w1', '16.x1', '16.bd1', '16.bq1'], 'core': '16.i1', 'coset_action_label': None, 'count': 4, 'diagramx': [6310, -1, 6325, -1], 'generators': [1, 164, 208], 'label': '256.26547.8.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bn1', 'projective_image': '128.1755', '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': '32.51'}
  • id: 64504101
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.202', 'aut_weyl_index': 64, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.i1', '4.q1', '4.x1'], 'contains': ['16.j1', '16.x1', '16.y1', '16.be1', '16.bs1'], 'core': '16.j1', 'coset_action_label': None, 'count': 4, 'diagramx': [9547, -1, 9570, -1], 'generators': [1, 40, 208], 'label': '256.26547.8.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bo1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504102
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.bp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 32, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.i1', '4.p1', '4.y1'], 'contains': ['16.k1', '16.x1', '16.z1', '16.bf1', '16.bt1'], 'core': '16.k1', 'coset_action_label': None, 'count': 4, 'diagramx': [7164, -1, 7182, -1], 'generators': [1, 188, 208], 'label': '256.26547.8.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bp1', 'projective_image': '128.1755', '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': '32.51'}
  • id: 64504103
    {'ambient': '256.26547', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 8, 'centralizer': '128.a1', 'complements': ['128.c1', '128.e1', '128.g1', '128.f1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.f1', '4.g1', '4.i1', '4.l1', '4.m1'], 'core': '2.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [4596, 4890, 4608, 4931], 'generators': [1, 2, 40], 'label': '256.26547.2.g1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.f1', '4.g1', '4.i1', '4.l1', '4.m1'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': '128.1755', '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': '128.1755'}
  • id: 64504104
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.bq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.o1', '4.v1', '4.x1'], 'contains': ['16.u1', '16.w1', '16.y1', '16.ba1', '16.bd1', '16.be1', '16.bh1'], 'core': '32.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [9074, -1, 9094, -1], 'generators': [1, 28, 164], 'label': '256.26547.8.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bq1', 'projective_image': '128.1755', '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': '32.51'}
  • id: 64504105
    {'ambient': '256.26547', 'aut_centralizer_order': 8, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.o1', '4.v1', '4.y1'], 'contains': ['16.v1', '16.w1', '16.z1', '16.bc1', '16.bd1', '16.bf1', '16.bo1'], 'core': '32.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [7757, -1, 7775, -1], 'generators': [5, 8, 164], 'label': '256.26547.8.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.br1', 'projective_image': '128.1755', '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': '32.51'}
  • id: 64504106
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 32, 'centralizer': '32.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1', '4.v1'], 'contains': ['16.ba1', '16.bb1', '16.bf1', '16.bg1', '16.cs1', '16.ct1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6440, -1, 6456, -1], 'generators': [1, 28, 240, 16], 'label': '256.26547.8.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bs1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504107
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 32, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1', '4.v1'], 'contains': ['16.bb1', '16.bc1', '16.be1', '16.bm1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9451, -1, 9473, -1], 'generators': [5, 8, 240], 'label': '256.26547.8.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bt1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504108
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 32, 'centralizer': '32.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1', '4.t1'], 'contains': ['16.bg1', '16.bi1', '16.bn1', '16.bt1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [7606, -1, 7623, -1], 'generators': [209, 28, 240], 'label': '256.26547.8.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.bu1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504109
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.j1', '4.r1', '4.z1'], 'contains': ['16.g1', '16.bl1', '16.br1', '16.cu1', '16.cv1'], 'core': '16.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [3669, -1, 3678, -1], 'generators': [3, 28, 16], 'label': '256.26547.8.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.bv1', 'projective_image': '128.1755', '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': '32.27'}
  • id: 64504110
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.j1', '4.s1', '4.ba1'], 'contains': ['16.h1', '16.bl1', '16.br1'], 'core': '16.h1', 'coset_action_label': None, 'count': 4, 'diagramx': [4040, -1, 4050, -1], 'generators': [3, 8], 'label': '256.26547.8.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.bw1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64504111
    {'ambient': '256.26547', 'aut_centralizer_order': 32, 'aut_label': '8.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.l1', '4.s1', '4.z1'], 'contains': ['16.j1', '16.bl1', '16.br1'], 'core': '16.j1', 'coset_action_label': None, 'count': 4, 'diagramx': [4336, -1, 4346, -1], 'generators': [3, 40], 'label': '256.26547.8.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.bx1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64504112
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.by1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.l1', '4.r1', '4.ba1'], 'contains': ['16.k1', '16.bl1', '16.br1', '16.cx1', '16.cz1'], 'core': '16.k1', 'coset_action_label': None, 'count': 4, 'diagramx': [3543, -1, 3551, -1], 'generators': [3, 188, 16], 'label': '256.26547.8.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.by1', 'projective_image': '128.1755', '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': '32.27'}
  • id: 64504113
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.bz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.z1', '4.ba1'], 'contains': ['16.i1', '16.bk1', '16.bl1', '16.cw1', '16.cy1'], 'core': '16.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [2894, -1, 2900, -1], 'generators': [3, 164, 208, 16], 'label': '256.26547.8.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.bz1', 'projective_image': '128.1755', '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': '32.27'}
  • id: 64504114
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '512.7538135', 'aut_weyl_index': 8, 'centralizer': '64.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.b1', '8.e1', '8.f1', '8.g1', '8.o1', '8.t1', '8.ba1', '8.bn1'], 'core': '4.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5915, 476, 5929, 480], 'generators': [1, 32, 4, 208], 'label': '256.26547.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.b1', '8.e1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 64504115
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.ca1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 32, 'centralizer': '32.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1', '4.t1'], 'contains': ['16.bm1', '16.bn1', '16.bp1', '16.bs1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9643, -1, 9666, -1], 'generators': [213, 8, 240], 'label': '256.26547.8.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.ca1', 'projective_image': '128.1755', '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: 64504116
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.cb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '4.z1', '4.ba1'], 'contains': ['16.i1', '16.br1'], 'core': '16.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [4188, -1, 4198, -1], 'generators': [219, 164], 'label': '256.26547.8.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.cb1', 'projective_image': '128.1755', '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': '32.27'}
  • id: 64504117
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.cc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1'], 'contains': ['16.bu1', '16.bx1', '16.cb1', '16.ce1', '16.cl1', '16.co1', '16.cq1', '16.cw1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2249, -1, 2254, -1], 'generators': [19, 32, 4, 208], 'label': '256.26547.8.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.cc1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504118
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.cd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1'], 'contains': ['16.bu1', '16.bv1', '16.bw1', '16.ca1', '16.ca2', '16.ck1', '16.ck2', '16.cq1', '16.cr1', '16.cw1', '16.cy1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [2102, -1, 2108, -1], 'generators': [3, 48, 4, 208], 'label': '256.26547.8.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.cd1', 'projective_image': '128.1755', '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: 64504119
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.ce1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1'], 'contains': ['16.bv1', '16.bx1', '16.cb1', '16.cc1', '16.cl1', '16.cm1', '16.cr1', '16.cy1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1957, -1, 1961, -1], 'generators': [3, 32, 4, 208], 'label': '256.26547.8.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '8.ce1', 'projective_image': '128.1755', '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': '16.14'}
  • id: 64504120
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.cf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.r1'], 'contains': ['16.by1', '16.ca2', '16.cd1', '16.cu1', '16.cv1', '16.cx1', '16.cz1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3293, -1, 3301, -1], 'generators': [19, 28, 48], 'label': '256.26547.8.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '8.cf1', 'projective_image': '128.1755', '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': '16.11'}
  • id: 64504121
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.cg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1'], 'contains': ['16.bz1', '16.cc1', '16.cf1', '16.cu1', '16.cx1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [3185, -1, 3193, -1], 'generators': [3, 28, 32], 'label': '256.26547.8.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '8.cg1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cg1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64504122
    {'ambient': '256.26547', 'aut_centralizer_order': 16, 'aut_label': '8.ch1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1'], 'contains': ['16.bz1', '16.ce1', '16.cf1', '16.cv1', '16.cz1'], 'core': '64.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [3408, -1, 3417, -1], 'generators': [19, 28, 32], 'label': '256.26547.8.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1', 'old_label': '8.ch1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ch1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64504123
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '8.ci1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.u1'], 'contains': ['16.cg1', '16.ch1', '16.ci1', '16.ck2', '16.cn1'], 'core': '64.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [779, -1, 781, -1], 'generators': [195, 218, 224], 'label': '256.26547.8.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '8.ci1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ci1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64504124
    {'ambient': '256.26547', 'aut_centralizer_order': 4, 'aut_label': '8.cj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 32, 'centralizer': '64.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.u1'], 'contains': ['16.cg1', '16.cj1', '16.cm1', '16.cp1'], 'core': '64.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [506, -1, 507, -1], 'generators': [211, 218, 240], 'label': '256.26547.8.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1', 'old_label': '8.cj1', 'projective_image': '128.1755', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cj1', 'subgroup_fusion': None, 'weyl_group': '16.14'}